Carlos Tevez struck late on to give the hosts a 1-0 win against unlucky Wigan in their FA Cup final dress rehearsal.
Argentine striker Tevez netted his 11th league goal of the season seven minutes from time to narrow the gap to 13 points between City and Premier League leaders Manchester United, who only drew at West Ham.
But after succesive victories against city-rivals United at Old Trafford and Chelsea at Wembley, Mancini felt his squad were running on empty.
The Italian told Sky Sports: "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.
"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."
And when asked about Tevez winning goal, Mancini said: "He's a top quality player and he played very well. He scored a fantastic goal.
"I think we didn't play well for 65 minutes. Instead the last 25 we played very well, scored a goal and created chances."
And the City boss feels confident that the Latics will remain in the Premier League come the end of the season.
"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."
"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."
Both sides went into the game on the back of emotionally-draining and energy-sapping wins in the FA Cup semi-finals and that showed in a low-key first half.
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.
Mancini dismissed a suggestion the title race could still be alive, although he did joke as he saw a replay of Robin van Persie's leveller for United on a pressroom TV.
He said: "This is not important now, it is finished.
"If they didn't score an offside (goal), probably..."