Carlos Tevez netted a hat-trick and there were also goals for Aleksandar Kolarov and David Silva as City thrashed Barnsley 5-0 at the Etihad Stadium on Saturday afternoon to make it through to the semi-finals.
Mancini was pleased to negotiate a potentially tricky tie and hopes City can keep going and clinch some silverware in either the FA Cup or the Premier League.
"It is important to have good concentration when you play this game because the other team has nothing to lose," explained the Italian.
"We want to do well always, in the Premier League and the FA Cup, and it is clear we want to go to the final if possible."
Wigan Athletic will join City in the draw for the last four and the remaining quarter-finals will be played on Sunday, with Millwall facing Blackburn Rovers and Manchester United entertaining Chelsea.
Mancini is in no doubt about what he would like to be the final line-up, adding: "It could be perfect because in the last two years United and City have been the best teams in England."