Manuel Pellegrini's men are facing a last 16 exit, heading to Camp Nou trailing 2-1 after a disappointing home loss.
But Toure and City continue to believe, and the Ivory Coast international said it was time to repay the club for their support.
"The club have been spending a lot of money to build the best players, try to make this club great and one of the top in Europe," he said.
"Now we have such a little bit of difficulty, but I can say we continue to work hard, because it's not the first time we've been in this situation.
"We have the belief of the team and as well we know our fans will back us again, because it's going to be a tough game against Barcelona and we need to turn back this tide, and we try to do it for the fans, and for the club, and for the people who continue to help us."
Toure also backed captain Vincent Kompany, who has come in for criticism in recent weeks, to bounce back.
The Belgium international was also partly responsible for City's shock 1-0 Premier League loss to Burnley, with his headed clearance falling for George Boyd to fire in.
"Well I think Kompany, for me, is ready. I think every player, at some time, have some doubt, some problems," Toure said.
"What is part of the football isn't part of the year. Sometimes you can find up and down, but I think he's fully focused, because this game is very, very important for us, for the club and as well for the fans.
"To pass this stage, we need to deliver, and I hope we will deliver."
