Manuel Pellegrini's men ran riot at Old Trafford, with the Bosnian international scoring twice and Yaya Toure bagging a late goal of his own in a 3-0 win.
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"I'm happy for the fans, because for them it is something special," he said, as quoted by the Daily Mirror. "We showed them again who is boss in the city!
"We knew before the game that this was an important game, especially because we had three games less than Chelsea.
"We knew this game was crucial to get another three points and now we are only three points behind them [Chelsea], still with two games to play more.
"It is a big result, but it's finished and now we need to concentrate on Arsenal [who City play on Saturday], which is another big game."
City have now won the last three consecutive Manchester derbies at Old Trafford.