"I agree, I've played against (Arsenal) 10 times and never lost, what more do you call me?" Mourinho, who once again won the tactical battle against Arsene Wenger at a rainswept Emirates Stadium, told reporters.
"What are they going to say? 'Funny, Funny Jose'? Ten times and they don't win once.
"I think Arsenal fans should just be happy, Arsenal are doing very well, they are in the Champions League and they have every reason to believe they can be back challenging for the title," added Mourinho.
It was easy to understand the home fans' frustration as their side missed the chance to move above Liverpool and return to the top of the table in time for Christmas.
Arsenal manager Wenger was also left frustrated after his 10th failure to beat Mourinho, feeling his side should have had a first-half penalty when Willian appeared to catch the ankle of Theo Walcott.
"I think it was a penalty on Walcott, 100 percent," Wenger said. "After that we played with great focus and concentration but in the second half we couldn't get the goal we deserved.
"They defended well, we didn't find our zippy moments. They were happy with a point and we weren't."
After a barnstorming start to the season Arsenal have picked up only two points from the last nine available, and the scars of a 6-3 defeat by Manchester City were still visible on Monday as they played without their usual freedom.
"Four games without a win doesn't help (confidence)," Wenger, whose side also lost to Napoli in the Champions League, told reporters. "We were a bit edgy at the start of the game but in the second half we took control.
"The defeats at Napoli and Man city left a little weight in our heads but we want to be strong enough to deal with."
Apart from Frank Lampard's volley which shook the Arsenal crossbar and a late chance wasted by Arsenal's Olivier Giroud, there was little in the way of goal attempts.
Mourinho, who left creative talents Oscar and Juan Mata on the bench, said that suited him just fine as Arsenal passed the ball around without penetrating.
"Arsenal were playing Arteta to Sagna, Sagna to Arteta, Arteta to Gibbs, Gibbs to Arteta and my players were just compact and had no problems," Mourinho said.
"The public were frustrated because they were expecting goals, chances and saves but nothing was happening. We had one big chances and many half chances, they had one big chance and no half chances. We played tactically very well."
Mourinho also played down Arsenal's complaints about John Obi Mikel's bone-jarring tackle on Arteta in the first half, which referee Mike Dean ruled fair.
"They like to cry," Mourinho said. "This is English football. It was a hard one, an aggressive one, but football is for men or women with fantastic attitude.
"It's true, there are other sports without contact. I respect them but football is a game of contact.
"English football, winter, water on the pitch, sliding tackles at speed but be proud. I think the referee did well."