Two sides packed with creativity and attacking flair failed to spark at Old Trafford on Monday night as they cancelled each other out.
Chelsea will be the happier of the two with a goalless stalemate, as they are now unbeaten through their opening three fixtures and back on top of the Premier League table.
Mourinho admits he had been hoping for more from his team as an attacking force in their latest outing, but considers anything taken from a trip to United to be a positive.
He told Sky Sports: "I think the result is fair. I think nobody did enough to be better than the opponent.
"I think we controlled the game for most of the time. For a match at Old Trafford, we didn't have real problems.
"Our counter-attacks and passes, to go from defensive situations to attacking situations, was not the best. We had very creative players in attack, very fast players in attack, but the ball possession was not the best, we lost simple passes. There were a lot of mistakes. In those terms, we didn't give what we could or what we should.
"But I told the players before the game: 'We want to win, we play to win, but if we don't win, we don't lose'. I think the players understood this completely.
"In the last five or 10 minutes, when everyone was really tired, I think my players kept a more defensive position and we went for the point, which is always a good point."
Mourinho opted to name a starting XI with no recognised striker, but maintains that he adopted the right tactical approach.
He added: "Playing with Fernando (Torres) didn't change a lot. For me, we didn't create more not because of the system, but because when we recovered the ball we lost so many easy passes. It was because of that.
"I shouldn't speak for them, but I think they also lost easy balls. We both wanted to win, but it was important not to lose. The goal didn't appear because that would have changed the course of the match.
"We have six points from our matches at home, some of our opponents have lost points already - Arsenal three points, City three points, Man United two points and us two points. After a difficult start we are fine."