Mourinho says he sent his players out to press Arsenal high up the pitch in the early exchanges, and it paid dividends as the Blues went two goals up inside seven minutes through Samuel Eto'o and Andre Schurrle.
"I think we started in an incredible way, seven minutes in, 2-0 and the game is over," he told BT Sport. "I think we started very, very strongly. We really wanted to try to make Arsenal feel not comfortable in the way they play, we tried to press immediately and recover the ball quickly.
The penalty incident saw Kieran Gibbs shown a red card, although it was actually Alex Oxlade-Chamberlain who handled Eden Hazard's shot in the area.
Referee Andre Marriner was roundly criticised for getting the wrong man, but Mourinho says he can sympathise with the official and that, ultimately, the decision to award a penalty and red card was correct.
"There were lots of people in the box, I think it was Eden with the shot. From the dug-out we see one player diving like a keeper and touching the ball with his hands, but from the bench we couldn't say which.
"My assistant was saying [Mikel] Arteta, the other one was saying Chamberlain and referee or the linesman said Gibbs. It's a difficult decision and if the fourth official says Gibbs... the penalty was a penalty, the red card was a red card, and unfortunately the wrong boy came off."
The Chelsea boss also hopes victory against Arsenal will get his side back on track after they were beaten at Aston Villa last weekend.
"We had momentum, but for some reason last Saturday the momentum stopped," he continued. "Now we are trying to build another momentum and the victory against Galatasaray was important, and against Arsenal... as Arsene Wenger was saying before the match, it was the most important game of the season for them.
"We don't say that, but we say it was a very important match for us because Arsenal are always an important rival, they are a rival also in the fight for the top four. When we get the top four we want to finish in the top three and qualify automatically for the Champions League and not have to qualify, so it was important to beat them today."
After again complaining that he is treated differently by the Football Association, Mourinho was asked if his side can win the Premie League title.
"If they let us," he joked.