The visitors appeared on course to inflict a first defeat on the Gunners since August when Milner scored the 50th Premier League goal of his career to open the scoring just after the hour-mark.
Arsenal battled back to earn a 1-1 draw as Alexandre Lacazette turned home a superb equaliser just eight minutes from time.
The draw extends Liverpool’s unbeaten start to the league campaign, with Jurgen Klopp’s side having previously drawn at Chelsea and at home to champions Manchester City, while winning 2-1 at Tottenham.
“This draw is different to Chelsea, for example, so there are ups and downs and things that we can learn,” Milner told liverpoolfc.com.
“But you can see we are moving forward as a team and we are defending well together. Again, that’s another learning curve for us – to see those sorts of games out.
“We are very disappointed really, which is a good thing I suppose, playing away at Arsenal.
“To be 1-0 up in the second half and not see it out, we are disappointed; with the chances we created we should have scored a few more goals.
“It’s pleasing we are creating those chances, but we could have been a bit more ruthless and maybe not put as much pressure on ourselves not to concede to win the game.”
Both sides had first-half goals ruled out for offside, Liverpool’s somewhat controversially, while Virgil van Dijk hit a post for the visitors on the stroke of half-time.
Arsenal’s record against their top-six rivals has been poor of late but Unai Emery’s side deserved to take a point from this game.
Having started his tenure as head coach with losses to City and Chelsea, the Spaniard has not tasted defeat since.
While the top sides have made impressive starts to the campaign, defender Rob Holding believes the Gunners have done a good job to keep up with them – the draw against Liverpool leaving them four points behind last season’s beaten Champions League finalists.
“We’ll take the draw and hopefully next time we’ll get three points,” said Holding.
“If everyone’s together, the sky is the limit. We’ll just keep pushing on. It’s a competitive league. Chelsea, Man City and Liverpool have all had flying starts and we’re right on their tails.
“We’ve just got to keep ticking away with the points and you never know what can happen further on in the season.
“There’s a really good team chemistry here and a winning mentality. We’re not losing and we’ll keep fighting until the end. We never give up, we’ll keep going and get what we deserve.”
After a stellar first half from the hosts it was actually the away side that went in front, James Milner capitalizing on a poor punch from Bernd Leno to sweep Liverpool into the lead.
The hosts levelled though inside the final 10 minutes – substitute Alex Iwobi threaded a fine ball through to Alexandre Lacazette and the Frenchman showed excellent composure to hold his nerve and bend beautifully past Alisson.
Here we rate the Liverpool players.
Alisson – 8: Composed amid a first half barrage from Arsenal, adept handling keeping them at bay. Distribution was also superb.
Trent Alexander-Arnold – 5: Not the full-back’s best game as he gave the ball away with alarming regularity. His 63.2 per cent pass success was the worst on the pitch.
Virgil van Dijk – 9: A colossus at the back as Liverpool found themselves under siege. Unlucky twice not to score. A genuine class act.
Joe Gomez – 6: Dealt adequately with everything Arsenal threw at the visitors. Overawed at times but stuck to task – led side with eight clearances.
Andrew Robertson – 7: A stellar athlete who never seems to fade. Not his usual best going forward while he also had to keep an eye on the marauding Bellerin.
Georginio Wijnaldum – 6: Had a quiet game and seemed overwhelmed with Arsenal’s pace. Did make two interceptions though.
Fabinho – 4: Looked all at sea as he tried hopelessly to shackle Ozil. Did lead Liverpool with three tackles, but still some way off being a regular.
James Milner – 7: As ever, put in a shift, and needed to as Liverpool’s midfield was overawed. Showed composure to put his side ahead. Three key passes.
Mohamed Salah – 8: Looked on it from the start and terrorised Kolasinac. Hasn’t been bad this season but seemed to take a step up here. Four key passes led Liverpool.
Roberto Firmino – 3: Unlucky to hit the woodwork, from which Mane’s strike was ruled out, but overall was woeful, indicative of current form. No shots on target from three attempts tells the story of his game.
Sadio Mane – 6: Harshly judged offside when tapping in Firmino’s rebound. Lively but wasteful and hesitant in possession, although he did create the confusion for the opener.
Xherdan Shaqiri – 6: Almost helped set up a second straight after Arsenal’s leveler, but cut-back was sent wide by Mane. That was more than Firmino had managed the entire game.
Joel Matip N/A: A late cameo for Salah.
Liverpool midfielder Georginio Wijnaldum thinks teams in survival mode can be trickier opponents than their Premier League title rivals.
The Reds overcame some stubborn resistance from Cardiff on Saturday, eventually prevailing 4-1 at Anfield – a result that arguably flattered the hosts despite a one-sided contest.
Cardiff showed little inclination to attack against a side that enjoyed 80 per cent possession and had 19 attempts on goal but it was not until the closing stages that Liverpool put the game to bed.
And Wijnaldum acknowledged that taking on teams happy to sit back and soak up the pressure presents a unique challenge – even if it was one Liverpool passed with flying colours in the end.
He said: “It’s more difficult than other games. When you play a top team they are trying to create chances, so when you have the ball you will have more spaces, they will try to press you.
“But with them they don’t really press. They were marking the spaces and their wingers played like left-back and right-back.
“It was difficult but we managed to score four goals.”
Mohamed Salah opened the scoring after 10 minutes with his fourth goal in the space of eight days – following on from his winner at Huddersfield and his brace against Red Star Belgrade in the Champions League.
The Egyptian has struggled to hit the heights he achieved in his debut campaign on Merseyside, in which he won the Golden Boot, but is gradually rediscovering his scoring touch.
Wijnaldum admits the recent signs are promising but said: “He has to continue to do that in a lot of games, not only the three games.
“He’s in a good way and hopefully he can keep it like that.”
Sadio Mane doubled Liverpool’s lead midway through the second half but Callum Paterson halved the deficit with a little under a quarter of an hour to go with Cardiff’s first effort on goal.
There were a few nervy moments but as Cardiff went in search of a leveller, they left themselves vulnerable at the back and Xherdan Shaqiri’s first Liverpool goal restored the two-goal cushion in the 84th minute.
Mane then added gloss to the scoreline three minutes later on the counter, prompting suggestions that Liverpool were jolted into action by Cardiff’s goal.
Wijnaldum added: “It’s difficult to say. Maybe, because we scored two goals after they scored one.
“That’s what we tried the whole game but also because they had the feeling they could score one more so we had more spaces.
“In the first half we didn’t have a lot of chances from counter-attacks.
“They were defending quite deep and even when the ball was going forward, they didn’t push up, they were standing behind because they know that we have fast players in the front.
“It was difficult to score when it was like that but after 2-1 they thought they had a chance which is normal and they were better in the game.”