Ever the pragmatist, Mourinho set up his side defensively and Chelsea were booed off the pitch after claiming a point, to chants of 'Boring, boring Chelsea'.
It was a recycling of lyrics which once were reserved for the Gunners and Mourinho insisted Arsene Wenger's men were the ones who should have felt the frustrations of their home supporters, not the visitors.
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."
Cech also hit back at the criticism, pointing to Arsenal's eight-year trophy drought.
"Well in the end you count the titles," he said.
"If you have figure skating where you are judged by how nicely your routine is then obviously that is one point, but football is about points and goals and you need to get points to win trophies."
The resilient rearguard performance was down to preparation, according to Mourinho, who aimed a verbal barb at another of Chelsea's title rivals, 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.
Mourinho believes six sides are in title contention, with Manchester City one point better off than his side, Tottenham six points off the pace and defending champions Manchester United two points further adrift.
Mourinho preferred romping away with the title during his first spell, but is enjoying the competitive nature of a Premier League season which has numerous twists and turns to come.
He believes it is imperative his transitional side are in contention, with future title battles in mind.
"I enjoyed it more in 2005 and 2006," he said.
"But for me it is fantastic. 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."
Mourinho reiterated he has no plans to delve into the January transfer market, particularly up front where he has been critical of his strikers. Fernando Torres, Samuel Eto'o and Demba Ba have a total of five Premier League goals this season, but he wants all of his players to be more ruthless in front of goal.
"We go with the same attacking players, with the same strikers," he added.
"We need the strikers to improve but we also need the other guys to be more effective in the way they transform half-chances into chances."
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