City returned to being 12 points behind leaders Manchester United with 10 games left thanks to Carlos Tevez's 45th-minute goal
A successful title defence looks unlikely, but Mancini just wants his players to keep picking up the points.
"We did a good performance and it was difficult," he told Sky Sports 1.
"For us it was important to stay 12 behind United, with 10 games left you never say never. Keep on winning and you never know, this is football.
"Last year nobody thought it was possible but 12 points in 10 games... If they lose four..."
City were solid at the back on Monday night, rarely looking like conceding, something all the more impressive considering the absence of captain Vincent Kompany.
"We are playing well and didn't concede a lot of chances," Mancini added.
"For me, Aston Villa are a good team and it is strange they're at the bottom."
Mancini also confirmed midfielder Jack Rodwell had injured a hamstring in the first half.
"Today [Monday] we showed we have a fantastic squad, we are sad with Jack but this is an important day for us," said midfielder Yaya Toure.
"Twelve points is a lot but it's not finished."
Toure's brother, Kolo Toure, was impressive in defence and added: "I'm doing my best for me, I love football and every time I have the chance I will give 100 per cent."
Villa remain in the bottom three and were made to pay for a moment of carelessness.
Ciaran Clark claimed a foul when Edin Dzeko robbed him in the build-up to the goal.
"I don't think it was a foul," manager Paul Lambert said on Sky Sports 1.
"I know what Ciaran was trying to do. You don't take a chance like that - you can't make that mistake.
"He's a young lad and he will come back stronger. He's been great over the season, at a really high standard, and he will learn."