The £100million pair made their first appearances in a Red shirt, playing 45 minutes apiece in the 7-0 friendly win at Chester.
Keita, in particular, slotted in seamlessly after the break and created one goal with his counter-pressing.
Klopp said he was helped by the fact former club RB Leipzig play a similar style and it would take Fabinho longer to adapt as Monaco’s football was different.
Asked what the pair will bring to the side, the Liverpool manager said: “Quality. It’s all good.
“You saw Naby comes from Leipzig and knows the football philosophy as it’s a similar one.
“He’s very sharp in the challenges, very quick in mind in these situations of counter-pressing, his impulses look kind of natural, which is good.
“Monaco played a completely different style, so Fabinho probably needs a few more days.
“But he’s a fantastic football player, a good passer, his challenges are good, a proper defensive midfielder with the option of being a number eight as well.
“If you want to be a part of our squad then you need to be good and these two boys are.”
Liverpool led 2-0 at half-time thanks a double from Wales international Harry Wilson but after the break Daniel Sturridge, who looked fit and sharp, scored twice, with Ryan Kent, James Milner (penalty) and Danny Ings completing the scoring.
Goalkeeper Loris Karius also had his first outing since his disastrous Champions League performance, where he was responsible for two of Real Madrid’s goals – with the club subsequently learning he had suffered a concussion.
The German made one good save, deflecting Jordan Archer’s shot over the crossbar and then late on in the first half did well to claim a high cross one-handed under pressure.
“It was a difficult save but he made that and it looked good and the high ball it was difficult,” added the Reds boss.
“Many goalkeepers would have dropped it and then everyone would have been ‘Oh that happened’ and it starts again.
“I need cool down the whole situation and play football and work on our weaknesses, use our strengths and everything will be good.”
The 2015/16 champions’ trip to Old Trafford on August 10 will be shown on Sky Sports, which will also televise Tottenham’s lunchtime (15:00 UAE ) visit to Newcastle the following day.
Also on Saturday, August 11, last year’s Championship winners Wolves meet Marco Silva’s Everton in a 17:30 (20:30 UAE) kick-off that will be on BT Sport.
In the first batch of Sunday games, Liverpool take on West Ham and Arsenal host reigning champions Manchester City, both of which will be shown on Sky Sports, while Southampton’s home game against Burnley has been pushed back to that date due to the Clarets’ possible involvement in a Europa League game three days earlier.
After a fourth-placed finish and defeat in the Champions League final, the ex-Reds captain has seen enough progress, combined with their early transfer activity, to suggest they can challenge champions Manchester City over a whole season.
“I think Liverpool are very close, I think they are knocking on the door,” Rangers boss Gerrard told Press Association Sport.
“I am delighted with where Liverpool are right now. Of course I wanted them to win the Champions League and I’m disappointed they never (did) but when you look at the big picture – and the journey they are on – it is a very exciting time being part of this Liverpool set-up.
“They have a terrific manager leading the charge and they have started making improvements and as a fan and an ex-player it is great to see.”
Asked whether they could close the 25-point gulf to City, having been only one of two sides to beat them in the league, Gerrard added: “The million dollar question.
“The gap has been big in terms of points not just for Liverpool but the chasing pack.
“I am sure Man City will strengthen again so it is a big ask but I think Liverpool are realistic title contenders going in next season.
“The form, how they played against City, they have proved they are capable.
“The challenge for Liverpool is can they do it over 38 games?”
Pivotal to that will be how Jurgen Klopp strengthens as – although his first-choice side was a match for any team – when injuries began to bite towards the end of the campaign, the squad looked lacking in depth.
Midfielders Naby Keita and Fabinho have already been secured and are set to make their first appearances in a pre-season friendly at Chester on Saturday.
Gerrard believes they will be pivotal in bridging the gap.
“They are recruiting very well. People want to come and play for this manager, people want to come and play for these supporters,” said the former midfielder.
“The signing of Fabinho will help. I am sure the other two or three targets they are after will help them be stronger and make the squad stronger and hopefully they can have a right good go at it.
“The starting 11 is very strong. I think by making signings naturally your bench becomes stronger.”
Goalkeeper is an area which fans want strengthening but Klopp seems set to continue with Loris Karius, who made two costly mistakes in the Champions League final even though it was later revealed he was suffering from concussion.
“Karius, to be fair to him, was getting stronger and stronger as the season when on,” said the 38-year-old Rangers manager.
“I think the key is does Jurgen think he has the mental strength to bounce back?
“Is he capable of parking that up, moving on and drawing from the experience?
“If Jurgen doesn’t think he is capable of bouncing back from that of course he will have to go into the market and get another goalkeeper but Jurgen knows him better than me.
“The easy thing to do is put a cross through his name and bin him but you have to remember he took Liverpool to the Champions League final.
“He is young so we don’t want to bin a good goalkeeper because he does have the potential to be very good.”