The champions were outplayed by the struggling Latics for large parts of a subdued Premier League clash at Etihad Stadium but Tevez's stunning intervention seven minutes from time snatched a 1-0 win.
The Argentinian turned on the edge of the area and slipped past two men before shooting into the top corner for his eighth goal in nine games.
It was harsh on Wigan, City's opponents in next month's FA Cup final, after Franco di Santo had forced a fine save from Joe Hart and Shaun Maloney had a shot cleared off the line by Joleon Lescott.
Mancini, when asked if Wigan could stay up, said: "I think so because they played very well.
"They don't deserve to be relegated and (Roberto) Martinez is a good manager. His team played very well.
"Wigan played better than us for 60 minutes. In the last 25 minutes, we played better, we had three or four chances to score but they probably didn't deserve to lose."
When asked if there may have been a hangover from his side's game on Sunday, Mancini said: "Probably yes. We spent a lot of energy against Chelsea and it was difficult."
With leaders Manchester United drawing 2-2 with West Ham on the same night after scoring a controversial equaliser, City cut the gap at the top to 13 points.