Carroll, an unused substitute in West Ham’s 4-1 home defeat against the Premier League champions last Sunday, left the bench early, and was then sent home from training by Moyes 24 hours later after he refused to apologise.
In his Evening Standard column, Moyes said he was “disappointed” with Carroll’s actions, while also taking aim at the club for leaking details of his training-ground summit with the forward.
“I was really disappointed in Andy,” Moyes said. “I don’t believe there was any excuse for what he did. He’s been fined but he has apologised, both to me and the players, and I think he understands it was wrong.
“The following day we had a discussion in the office at (West Ham’s training ground) Rush Green. I told him it was unacceptable and sent him away.
“Within an hour, it seemed, it was out there for public consumption, which is also disappointing. Things go on all the time at clubs and there needs to be some privacy.”
Moyes added: “To be fair, Andy texted me later and apologised. I told him he needed to come in the following day and speak to me and the players and he did that. Since then, he’s been back training.
“Initially, I wasn’t aware that he had left the bench and I didn’t hear what had happened until after the game. I just believe strongly that everyone is part of the team and everyone has to show that all the time, especially at this time of the season.”
Speaking at his press conference ahead of West Ham’s vital Premier League match against Leicester, Moyes confirmed Carroll would be in his squad to face the Foxes at the King Power Stadium.
“We have moved on,” Moyes said. “We’re quite happy that it is done in dusted. He was in the squad last week and that was why he was on the bench. He will be in the squad this weekend as well.”
West Ham remain in a precarious position in the Premier League, just three points above the relegation zone, following successive 4-1 defeats to Arsenal and City.
The Hammers are without a win from their last four games, and travel to Leicester before matches against Moyes’ former clubs’ Manchester United and Everton at the London Stadium.
“We have got three games to win,” Moyes said. “If we can win all three of those games then we might find ourselves quite high up the table so that is what we are going to try to do.
“The mood is good. We were really disappointed with how we played, even against the champions, but overall they are keen to put it right.
“The motivation and attitude has been very good. They know exactly what is at stake so we will all work together and try and get a result.”
Wenger, who is bringing down the curtain on his 22-year Arsenal reign at the end of the season, will take to the home dugout as manager for the last time on Sunday when Burnley travel to the Emirates Stadium.
The match is a Category C fixture – the lowest of three tiers in Arsenal’s official Premier League ticketing structure – with prices ranging from £26 to £38.50.
The club’s website crashed in the moments after Wenger announced he would be leaving last month as Arsenal fans scurried to buy the final remaining tickets for the historic match.
But supporters without a ticket now face having to spend well over the odds to see the 68-year-old Frenchman’s last home game.
Ticketbis, a secondary ticketing online market, claims to have a range of seats available from £143 to a staggering £1,800.
The most expensive tickets are being advertised in the lower tier of the East and West Stands at the Emirates Stadium, which would have been sold to supporters for just £28.50. The ticketing website also claims prices for the match are increasing.
Tickets for Sir Alex Ferguson’s final match in charge of Manchester United also changed hands for eye-watering sums. A seat for United’s game against Swansea at Old Trafford in 2013, the Scot’s last of his 27-year tenure, was reportedly advertised for nearly £3,000.
Arsenal face Atletico Madrid in the second leg of their Europa League semi-final on Thursday night.
The two teams drew 1-1 at the Emirates last Thursday after Antoine Griezmann cancelled out Alexandre Lacazette’s strike.