Villa dominated the game from start to finish and secured their first victory over City since 2013 thanks to a deflected shot from Leon Bailey in the 74th minute.
The result left Pep Guardiola's team fourth on 30 points after 15 games - six points behind leaders Arsenal - and without a win in their last four league matches.
City last went four Premier League games without a win in April 2017.
"We have to use the hurt and the pain that is within us, our stomachs, our brains, wherever it might be, as motivation and fuel to put things right. I think everyone has that desire," Stones told City's website.
"We've been in these positions in previous seasons. I don't think we or everyone should be hyping about what is going to happen. I think we have to stay calm as a team, which we will do tomorrow once we've analysed it and settled down emotionally."
City next travel to face 17th-placed Luton Town on Sunday.
