Neither side managed to create a really good chance in a tentative 90 minutes of football that saw Chelsea begin the match without a recognised striker on the pitch.
Mourinho's tactics appeared to be negative, but he insists that his side played to win the game and that the lack of openings was down to errors on the pitch.
"We did enough to be better than the opponent. We controlled the game for most of the time. We did not have real problems. We made simple mistakes. In terms of attack we did not give what we should," Mourinho told Sky Sports News.
"We play to win but if we don't win we don't lose and I think the players understand this completely. Both teams gave everything and I think towards the end my players went for the defensive position and to get the point.
"We didn't create more, not because of the system but because we lost so many easy passes. I felt United also lost five or six easy balls. It was a difficult match for both of us. We both wanted to win and both did not want to lose. It was a really big, big match but without goals. But we have six points from our matches at home. Some of our opponents have lost points already, so after this difficult start we are fine."
The result leaves Chelsea top of the Premier League table by one point having played a game more than their nearest challengers Tottenham Hotspur and Liverpool.