Carlos Tevez's goal late in the first half was enough to give City victory at Villa Park on Monday to leave Mancini's side 12 points behind leaders Manchester United.
United remain firm favourites with 10 games to go but Mancini wants his players to keep winning games in hope of pulling off a repeat of last season's late run to the title.
"We did a good performance and it was difficult," the Italian told Sky Sports. "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 midfielder Yaya Toure echoed his manager's sentiments.
"Today we showed we have a fantastic squad, we are sad with Jack but this is an important day for us," said Toure. "Twelve points is a lot but it's not finished."
The defeat means Villa remain in the bottom three in 18th place, level on points 17th-placed Wigan but with a worse goal difference.
Mancini was impressed by the home side, though, and backed them to avoid relegation.
"For me, Aston Villa are a good team and it is strange they're at the bottom," he said.
Mancini also confirmed that midfielder Jack Rodwell had injured a hamstring in the first half of the game.