Wigan replicated their FA Cup heroics from last season's final to beat City 2-1 at the Etihad Stadium thanks to Jordi Gomez's penalty and James Perch's second-half strike.
Samir Nasri's volley ultimately counted for little, and Pellegrini was quick to hold his entire side accountable for defeat.
City will now travel to Camp Nou on Wednesday for their UEFA Champions League last 16 second leg tie trailing 2-0 from the initial game.
But the Chilean has laid down the gauntlet to his side, and remains hopeful that they can secure a quarter-final spot in Europe.
"I think we cannot be eliminated in the FA Cup here at home against Wigan," Pellegrini told BT Sport. "We had three or four clear chances at least to draw.
"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.
"We are in the last part of the season. It is important to react from tomorrow until the end of the season.
"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."
