Mourinho accused West Ham of "19th century" football, while Allardyce hit back declaring "I don't give a s*** about Jose".
But writing in the London Evening Standard, Allardyce said: "His comments apart, Jose was okay after the match. He seems less tense this time than during his first spell in England, perhaps more sociable. He says he is the Happy One now and perhaps he is.
"He has achieved so much in his life, he should be happy. He knows how to change his teams and when to change them. You survive in this management game only if your man-management skills are good and you are tactically aware. Jose has both those qualities.
"What he said about us I take as a great compliment. Jose invented parking the bus, don’t forget. I’ve played against his Chelsea side at Stamford Bridge when they’ve gone 1-0 up and he has put on two defensive midfielders. I’ve seen him play direct to Didier Drogba when it’s needed.
"It’s perhaps a bit sad when he says things about teams who have played well against Chelsea but that is just his character. The last thing I want is for opposing managers to pat me on the back and tell me what attractive football my team have played — after we’ve lost 3-0."