Toure scored the second in City's 3-0 win over Viktoria Plzen and the Ivory Coast midfielder says that they need to show they are a match for Europe's finest after their previous displays in Europe.
"The last two years were quite disappointing for us, for the fans and for the club," he told Sky Sports.
"It's important for us to prove to the fans who love Man City that this year is going to be our year. Our most important target is getting through to the second round and showing improvement."
Edin Dzeko opened the scoring in the Czech Republic and he felt the win was the ideal way for them to begin in Group D.
"It's the perfect start," Dzeko added.
"The last two years we didn't do that in the first game and now we did. Especially coming away from home, we know it's always difficult to play away in the Champions League because every team is very strong and Plzen showed in the first half how they can play football.
"We're very happy to go home with the three points."
Dzeko was again given the nod to start the game ahead of summer signings Alvaro Negredo and Stevan Jovetic, and the Bosnian was happy to have the confidence of the new manager.
"It's very important," he said. "I've already said it before the season started. But I think we have a very good squad with some new players who have brought a lot of quality to our team and of course there are a lot of games until the end of the season. Everyone will get a chance to play."