Toure, City's midfield talisman, scored a hat-trick in Saturday's convincing 5-0 win over 10-man, relegation-threatened Fulham.
The victory lifted Manuel Pellegrini's side to third in the Barclays Premier League, six points behind leaders Chelsea with three games in hand.
Toure set up the win by scoring the first two goals from the penalty spot and then curling home a sublime third at the Etihad Stadium. Fernandinho and Martin Demichelis added gloss to the scoreline late on.
Toure, the former Barcelona midfielder who also scored a brilliant goal to help win the Capital One Cup earlier this month, told City TV: "I came to the club to make history and I hope to continue to the end of my contract.
"I think the club and the fans need trophies, need history and need great players to come here and try to make this club great.
"We have the team, we have the players, we have the manager as well.
"I hope at the end of the season we lift this trophy for these fans who love City."
Toure's treble took his tally for the season to 20. He is the third City player to reach that landmark this season after Sergio Aguero and Alvaro Negredo while Edin Dzeko, who missed the game through sickness, has 18.
The Ivory Coast international attributes his fine goalscoring form this season to the confidence placed in his offensive ability by attack-minded manager Pellegrini.
The 30-year-old said: "He gave me more freedom up front, he gave me more confidence to attack more.
"When you play full attack you can leave some space and it is very hard because when we win it is fine, but when we lose we get some criticism by some people who think they understand football more.
"But that is part of the job, that is why we love football. We are very happy to score five goals in front of the fans and I hope we will continue to the end."
City were not at their best but were still far too strong for Fulham.