Lescott's spell on Merseyside ended on a sour note when he was dropped by Everton manager Moyes ahead of last week's Europa League clash for having a "poor attitude".
But the Birmingham-born defender said at his unveiling: "I was disappointed in the comments, I feel they're inaccurate.
"I'd like to address them at a later date and talk more positively about my move here.
"I don't think I disrespected any of the players. If I did, I apologise."
City's bid, reportedly worth £22million, was accepted by Everton on Sunday but there was a brief delay to the England international's transfer going through as a minor wrangle was resolved.
Lescott was part of the Toffees team which lost 6-1 at Goodison Park in their Premier League opener earlier this month, with the former Wolves man coming in for particular stick over his display.
He added: "I'd like to think they thought I gave my all when I played.