The Blues were booed off the pitch after claiming a Premier League point, to chants of 'boring, boring Chelsea', but Mourinho has defended his side's tactics and insisted the Gunners were the ones who should have felt the frustrations of their home supporters.
Mourinho said: "I think boring is a team that plays at home and cannot score a goal. That's boring.
"If somebody was boring, they were boring because Petr Cech made zero saves.
"You go to your stadium and you fill your stadium, in weather like we had on Monday, to see victories. There is not a home fan in any club in the world who goes to the stadium and expects his team not to win."
The resilient rearguard performance was down to preparation, according to
Mourinho, who also took a swipe at another of Chelsea's title rivals, Premier League leaders Liverpool, who play at Stamford Bridge on Sunday.
"We played Sunderland last Tuesday and we had one week to work which we didn't have since the summer," Mourinho added.
"I had three days to work tactically. I worked on everything because it was a special week for us. It was the kind of week Liverpool has every week."
Chelsea enter the Boxing Day contest with Swansea in fourth place, two points behind Liverpool, the leaders on goal difference from Arsenal, and Mourinho says he is enjoying the competitive nature of the Premier League.
"For me, it is fantastic," he said. "The pressure is there. I have told the players they have, some of them, to learn how to cope with this situation. Because they have to learn.
"For me, it is not a problem. For some of the guys it is not a problem. But for them, now, they have to learn how to express themselves on the pitch in this situation.
"When you are 20 points behind the leader, you can play at home one day and win 6-0. But what does that mean? It means nothing.
"What means something is when you are fighting for the title, play a fantastic match and score the winning goal.
"That is the way, especially young players, grow up quickly. They have to grow and I think I'm the right guy to teach them how to cope with this situation because it's a situation I enjoy."