City won the FA Cup final dress rehearsal at Etihad Stadium thanks to a brilliant late goal by Carlos Tevez but it could have been a different story if Roberto Martinez's side were not so wasteful.
Mancini knew it was an average performance against the 18th-placed Latics side who he feels are good enough to stave off relegation.
"We worked really hard because Wigan played really well and every game we play against them is difficult because they play football and they like to win every game," he told Sky Sports.
"I don't think we played very well because we were so tired. Only in the last 20-25 minutes we played better.
"I think they will stay up because I'm sure they will do a good job from now until the end. They play very well and Roberto Martinez deserves to stay in the Premier League."
He added: "It was hard work because we were so tired because we played two important games in five days and we played the last game three days ago (FA Cup semi-final).
"It was a difficult game but we knew this before the game. Wigan play good football, they play really well.
"Wigan played well every time they want to play to win because they have a good manager."