Arteta was on the receiving end of two ankle-high tackles from Mikel and Ramires in Monday's night 0-0 draw at the Emirates Stadium, while Arsenal might have had a penalty after Willian's challenge on Theo Walcott in the first half.
Asked about Arsenal's reaction to the decisions which went against the hosts, Mourinho said: "They like to cry, that's tradition.
"I prefer to say that English people - and I give one example, Frank Lampard - would never provoke a situation like that.
"Players from other countries, especially some countries, they have that in their blood.
"Foreign players are bringing lots of good things, but I prefer English blood in football and English blood in these situations is 'come on, let's go'."
Asked specifically about Mikel's tackle, Mourinho insisted it was fair.
He added: "It was a hard one, an aggressive one. Football is for men or for women with fantastic attitude.
"There are other sports without contact and fantastic sports and sports that demand a lot from the players, but no contact.
"Football is a game of contact. English football, winter, water on the pitch, the sliding tackles become at a fantastic speed. So be proud, play with proud."
Chelsea set up defensively in the clash and shackled Arsenal, with the home fans booing the Blues off and labelling Mourinho's men 'boring' at the final whistle.
Responding to the 'boring' chants, Mourinho, who is still to be beaten by Arsene Wenger's Arsenal in 10 attempts, said: "I'd agree. I played against them 10 times and I never lost.
"'Funny, funny Jose'. Ten times, they don't win once. What do you want to call me?"
The Portuguese was content with the result which took his side fourth, two points behind Liverpool, who lead Arsenal on goal difference.
Mourinho added: "Happy with the result? I would say not unhappy. We came to win, we wanted to win, we didn't want to lose. It's very important not to lose, because if we lose we are five points behind the leader.
"And, with a point, we are two points behind both leaders. That's a completely different picture. We tried to win, but we are not unhappy with the point."
Mourinho believes referee Mike Dean performed well; Wenger did not.
The Arsenal boss said: "I don't think he had a great game at all."
Wenger declined the opportunity to elaborate and did not criticise Dean for failing to take clear action on Mikel's tackle.
"I have to watch that again on television," Wenger added.
"On the pitch it looked bad, but the referee was in a good position."
Wenger felt Arsenal deserved a spot-kick in the first half.
He added: "I think it was a penalty. Honestly. If I'm wrong, I apologise.
"I've not seen it again, but it looked like a penalty.
"They defended well, were well organised, and we didn't find our zippy movements to play between the lines as we can."
Mourinho was content with a point, but Wenger wanted more.
He added: "Overall, they were happy with a point and we weren't. But we couldn't take our few chances we created.
"We dropped two points tonight and that's what we want to focus, to win the next game (at West Ham on Boxing Day)."
It was Arsenal's fourth successive match without a win.
"We're going through a patch where it's a bit more difficult, but part of a successful season is how you deal with that.
"The spirit of the players is unbelievably focused. There's a great desire.
"But let's be serious: if after the first game against Aston Villa (when Arsenal lost) I'd told you we'd be top of the league at Christmas, you'd have told me I was absolutely mad.
"We are where we are. The last three games have been a bit more difficult, but we have played Everton, Man City and Chelsea."