Mancini's side have no room for error as they travel to Villa Park on Monday looking to keep their slim Barclays Premier League title hopes alive.
After a deserved victory over Chelsea last weekend, City will be expected to brush aside the relegation-threatened midlanders.
But the champions came unstuck at another struggling side, Southampton, last month and Mancini is wary of some of the talent at Villa Park.
The Italian said: "Aston Villa are in a difficult situation. I don't know their situation very well but for me they have good players. Maybe they have young players and this is the reason they fight against relegation.
"But it is my opinion they have good players and probably they don't deserve to stay there."
City went top of the table when they thrashed Villa 5-0 at the Etihad Stadium in November.
The defence of their crown seemed on target then but Manchester United soon edged back in front and City have not been able to claw points back since losing to their derby rivals in December.
They have gradually slipped further behind, bringing Mancini's future into question, but the City boss is determined not to let the title slip away quietly.
After memorably overturning an eight-point deficit in the final six games last season, City are certainly experienced in chasing apparent lost causes.
Mancini said: "When we have another 11 games and it is impossible (to give up). We should do our best from now to the end and after we will see what happens."
City's 2-0 win over Chelsea, with brilliant goals from Yaya Toure and Carlos Tevez and a penalty save from Joe Hart, was a defiant reminder of their abilities after the Southampton debacle.
Another positive aspect was the performance of midfielder Jack Rodwell, who finally showed City fans a glimpse of his talent.
The 21-year-old has hardly got going at Eastlands since his £12million move from Everton last summer with his uncertain initial appearances followed by a three-month lay-off with hamstring problems.
Mancini said: "I am happy for Jack because he is a good guy and he deserves to play a good game.
"He had a lot of injuries and big problems and for this reason he did not play a long time. He played only for 60 minutes but he played well."
Rodwell produced an energetic box-to-box display before being replaced in the second half when Mancini felt he was getting tired.
The quality of last summer's signings may have been a source of consternation this season but Mancini is convinced there is plenty more to come from Rodwell.
Mancini said: "We bought him last summer, for this reason, because he is young and we think he can improve a lot."
City again look likely to be without captain Vincent Kompany at Villa Park.
The 26-year-old defender has not yet returned to full training after suffering a calf injury in the FA Cup fourth-round win at Stoke five weeks ago.
City had expected him back by now but he has also had problems in his opposite calf and next week's cup quarter-final against Barnsley is a more likely return date.
Midfielder Gareth Barry is fit to face his former club after two games out with an ankle injury.