The victory comes on the back of a heavy 4-0 defeat at Chelsea, Mourinho's former club, and he was pleased to return to winning ways after such a crushing result.
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Manchester United boss Jose Mourinho says his side deserved to beat Manchester City
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Juan Mata scores winner for Manchester United
"I'm happy the players did everything and they deserved to win," Mourhino told Sky Sports. "In the last week everything went against us but we are professionals.
"The fans felt deeply such a negative result and today was a good chance to clean that feeling because it's a derby and knock-out and to win against Man City gives everyone a better feeling.
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Jose Mourinho says Manchester United worth winners over Pep Guardiola's Manchester City
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"I'm especially happy for the players and fans.
"In the last seven (games) we lost one. It was a big defeat that the numbers the history of this club doesn't deserve.
"When I'm in a club my heart belongs to the fans and I felt especially deeply for them."