The champions have responded well since a dismal defeat at Southampton all but ended their hopes of retaining their Barclays Premier League crown last month.
City thrashed Leeds in the FA Cup and deservedly overcame then third-placed Chelsea 2-0 but leaders Manchester United remain in complete control of title race.
Mancini's men next travel to struggling Villa knowing any they cannot afford to let the intensity drop.
The Italian said: "For us, it will be important. If we don't beat Aston Villa, it is like we didn't do anything against Chelsea.
"For this reason it is important to beat Aston Villa and afterwards continue to go.
"The season is not finished. It is impossible we can think it is finished now.
"There are 11 games to the finish. It is our job to play all the games 100 per cent and try to win always."
City and Mancini, of course, have experience of chasing apparent lost causes having memorably fought back to pip United to the title on goal difference last season.
Mancini said: "I was not strong in mathematics in school, but with 11 games to play - 33 points - everything is possible.
"Last time we won the title from six games to go, eight points (behind). I think everything is possible."
City captain Vincent Kompany seems unlikely to return to action at Villa Park.
The Belgium defender has missed five games since suffering a calf injury in the FA Cup fourth-round win at Stoke just over a month ago.
It had been hoped the 26-year-old could return against Chelsea but the problem has lasted longer than expected and Kompany has also had trouble in his opposite calf.
Mancini has not yet ruled him out for Monday but the cup quarter-final against Barnsley next week is now looking a more realistic comeback target.
Mancini said: "Vinny is getting better in this moment.
"We hope we can recover him for the next game. We will try for Aston Villa for Monday but it is difficult because he did not train with the team, he trained with the physio.
"We hope for the FA Cup.
"The calf is a difficult injury because you think you are okay and then you have a problem. The calf is a strange injury."
Former Villa midfielder Gareth Barry should be fit to face his old team after two games out with an ankle injury.
Mancini said: "He has trained with the team the last two days and I think he will be ready."