City challenge for a fouth place finish was kept firmly on track as goals from Roque Santa Cruz and Carlos Tevez helped them to a 2-1 win at Craven Cottage on Sunday afternoon.
"We deserved to win the game," Mancini said after the match.
"We created a lot of chances but it wasn’t as comfortable as it perhaps should have been.
"We had two or three chances in the second half and if you don't finish off the game there's always a chance something can happen.
“This was a great win for us because this is a difficult ground to come to, not many teams win here.
"We must think game after game. We have won this but on Wednesday we have a hard match against Everton.
"There will be a fight until the end of the season."