Toure has described next Monday's derby with United at the Etihad Stadium as one of the most important games in the club's history.
The midfielder and other City players found out about United's shock 4-4 home draw with Everton while on the coach to Molineux for Sunday's clash with Wolves.
A 2-0 win, thanks to goals from Sergio Aguero and Samir Nasri, means City are only three points behind United and with a superior goal difference.
Toure said: "United's result was amazing. It was an unbelievable day for us with United dropping points at home. For me, it was strange.
"We found out about it on the bus on the way to Wolves. It was quite unbelievable and we now have to try and take advantage.
"We did the first part by beating Wolves but we have to settle down and continue to work hard because United still have three points more than us.
"We have to play them at home and, if you look at the record of United, they are very strong away and it will be a very difficult test for us.
"I think this year the club need to win the cup (title) and it will be difficult.
"But we need to win this derby because it will be one of the most important games the club have had."
Toure praised the City players for being able to take advantage of United's slip-up by disposing of relegated Wolves.
He said: "People say we looked nervous at stages of the game and we have a lot of young players and not so many experienced ones.
"When your big rivals drop points at home, and you have to win your game, it is quite difficult.
"But with the players we have, it can make the difference all of the time with the likes of Aguero, Tevez and Nasri, and we did the job."
Toure knows City still have plenty of work ahead if they are to win their first top flight title since 1968.
He said: "They are very difficult games to come. We have United, then Newcastle who are playing well at home.
"These games will be very tough until the end of the season, and QPR are playing well as well.
"But, with the team we have, if we win something this year it will be fantastic for us."
City manager Roberto Mancini continues to play down his side's chances despite United's unexpected setbacks via defeat at Wigan and letting slip 3-1 and 4-2 leads against Everton.
But he is happy with the improvement in his side compared to last season.
Mancini said: "We have another chance but they have a bigger chance than us at this moment.
"After the derby, the games United have left are not as difficult as the ones we have to play.
"We have improved a lot from last year. This is important if you are building a team. If you win, you are happy, for sure. But if you are improving, then that's important."
City striker Mario Balotelli will be available for the derby after serving a three-game ban and Mancini believes he will have an important role to play.
He said: "I'll be happy to have Mario available. It's one player more for next week.
"Mario scored two goals against United at Old Trafford. He's a very important player for this game."