Following Mancini's sacking, a below-par City lost to Norwich in their final competitive game last Sunday and caretaker boss Brian Kidd admitted the players, now on a post-season tour of the United States, were drained by developments.
City's campaign finally reaches its conclusion as they take on Chelsea in a friendly in New York's Yankees Stadium on Saturday night and Lescott expects the players to quickly bounce back.
He said: "It's been difficult for everyone but it is important as a player you understand that no matter what happens you need to keep striving to improve every game. We'll continue to do that.
"The decision has been made by the club and we have to respect that as players.
"We play for Man City. They have seen fit to part ways with Roberto and we have just got to get ourselves right for the new manager."
Lescott's season still has a little way to run having been named in the England squad for upcoming friendlies against the Republic of Ireland and Brazil.
But the intensity has notably dropped this week as the players have undertaken a number of promotional activities on behalf of the club in New York.
They then played out an entertaining first friendly against Chelsea in St Louis, with City emerging 4-3 winners after falling 3-0 behind.
"It was not a competitive game in that sense, but it was entertaining, which is what the fans want to see," said Lescott, who himself was rested.
"It was good. It was a friendly atmosphere and I am sure we kept them entertained.
"You've got to finish the job off. That is what we are trying to do. We are representing Man City at the end of the day.
"There hasn't been much training going on. It's been a commercial trip. We've got one more game to go but it's been a productive week."