Chelsea boss Mourinho said he was happy with the Blue's performance despite Robin van Persie's dying minute strike which saw the Red Devils secure a point at Old Trafford.
Both Chelsea and Manchester United were not able to score a goal in the first half but Didier Drogba broke the dead-lock in the 53rd minute after he headed home a Cesc Fàbregas corner-kick.
But Manchester United striker Van Persie lashed home a leveller in the dying minute after Branslav Ivanovic had been shown a second yellow card for tripping Angel di Maria.
However, Mourinho's side are now four points clear at the top of the Premier League table, and the Chelsea boss believes there were plenty of things to be happy about during the match.
“We don’t look to others, we look to ourselves,” said José Mourinho.
“Old Trafford is one most dangerous fixtures we’ve had. The result is not the result we want, but the way we performed means we don’t need to look to others.
“After nine matches, to be top of league with four points difference. We have also played away at Manchester United and Manchester City.”
Mourinho continued: “The second half was much better. From the start of the first half we showed we wanted to win.
“In the second half we didn’t give them chances they wanted. To come here to Old Trafford the way we did – it was fantastic to my boys.”