City's 2-1 win over Chelsea at Wembley booked a return trip to face neighbours Wigan on May 11.
Strangely, the Latics also provide City's opposition on Wednesday, when they will attempt to delay United's title celebrations, which could be launched as early as next weekend.
Mancini does not want that to happen. For whilst he has given up any hope of the Blues retaining their crown, he is not ready to hand the trophy over just yet.
"United deserve to win this title but we deserve to fight until the last two or three games," said Mancini.
"Our target at the start of the season was the Premier League and FA Cup.
"We knew the Champions League would be difficult because we had a difficult group.
"We had a chance to win another Premier League if we worked well last summer. But we didn't. We made some mistakes.
"We are frustrated about that but we know we are a good team.
"We want to win the FA Cup final and we have a chance to finish second and show we don't deserve to be 15 points behind."