The Belgian defender was dismissed after just 11 minutes at the KC Stadium for dragging down Tigers' striker Nikica Jelavic.
However, Manuel Pellegrini's 10-men were inspired, despite the setback, as goals from David Silva and Edin Dzeko handed them three crucial points to keep them in the hunt for the Premier League title.
And France international Nasri admitted the sending-off made City even more determined to show their quality.
"When your captain gets a red card, you just want to show that you can do it without him and as well do it for him," Nasri said.
"You want to fight to the end and that's what we did.
"Do we only need 10 men? I don't think so but it was good to show everyone that we are back on track, that when everyone plays for the team, it doesn't matter if we have 10 or 11, we can win games because we have quality."
Despite Silva's inspirational display, Nasri feels City have several players that are capable of changing the course of a game.
"I think we have a team with plenty of players and if you want to win the league then you have to think about the team rather than just one player who can make a difference."