Goals from Jordi Gomez and James Perch fired the Championship club into a semi-final tie against Arsenal at Wembley as City failed to find an equaliser after Samir Nasri's strike.
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"I think we cannot be eliminated in the FA Cup here at home against Wigan. We had three or four clear chances at least to draw," Pellegrini told BT Sport.
"But Wigan played well and had a lot of intensity and they deserve to continue.
"I don't like to divide defence and attack but we could do more with both goals Wigan scored but also we didn't play very well in attack."
City now travel to Barcelona for the second leg of their Champions League last-16 tie on Wednesday and must overturn a 2-0 deficit in order to progress to the quarter-finals.
Pellegrini's men are also nine points behind Chelsea in the Premier League but have three games in hand over Jose Mourinho's side.
"We are in the last part of the season. It is important to react from tomorrow until the end of the season," said the City boss.
"We must go now to Barcelona and try to continue in the Champions League. We know it's difficult but we must try. And then we must try to finish in the Premier League and be top of the table again.
"I repeat what I have said every week. we are going to try and win every match we play and at the end of the season we’ll see who scores more points.
"It's important to react immediately because we have important things from now until the end of the season."