A 3-2 win at Everton on Saturday lifted Manuel Pellegrini's men to the top on goal difference, City's being nine better than second-placed Liverpool's.
Tour feels leading the way with just two league matches remaining meant his side were expecting to win the crown.
"We definitely expect to win it – as a team at the top you always expect to win," Toure said.
"We have worked so hard this year and if we don't win, it would be a massive disappointment for us, for the fans and for the club as well.
"We need to do the job. The new manager has come in and tried to perfect things, and we have worked hard in training. Now we need to deliver in these two games."
City have home matches against Aston Villa and West Ham to finish the season, and they will be expected to win both.
Toure wants to avoid a repeat of the 2011-12 season, when City clinched the title thanks to a last-gasp Sergio Aguero goal against QPR on the final day.
The Ivory Coast international said his team needed to get the job done in more convincing fashion this season.
"We have two games at the Etihad (Stadium) and the most important thing is to do the job and win those games," Toure said.
"QPR were a relegation side and when you look at West Ham and Aston Villa they have good players and managers and want to show the fans they can do the job.
"We will have to be clever and concentrate, and even if we have a good result on Wednesday we have to do it all again on Sunday.
"It will be massive if we win it, definitely bigger than two years ago, because it means we will have won two trophies.
"The target was always to win something, but for us the League Cup is not enough. The Premier League is always our target, so now we need to do a job when Villa come to our stadium."
