West Ham showed limited attacking intent as they claimed an important point in their battle for survival, having been penned back by Chelsea for long periods on Wednesday.
After a tenacious defensive display frustrated the hosts, Mourinho complained to Allardyce that West Ham played "football from the 19th Century".
And the former Bolton and Blackburn boss delighted in the fact that his opposite number had also shared those thoughts with the assembled media.
"I knew he would, he can't take it can he? He just can't take it because we've out-tacticed (sic) him, we've out-witted him. He just can't cope!
"He can tell me all he wants, I don't give a s***e to be honest with you.
"I love to see Chelsea players moaning at the referee, trying to intimidate him; Jose jumping up and down saying we play c*** football. It's brilliant when you get a result against him… so hard luck Jose!"
Allardyce took considerably less cheer in revealing that Joey O'Brien is facing around three months on the sidelines with a dislocated shoulder suffered during the match – an incident that continues West Ham's unfortunate injury record this term.
"Joey has dislocated his shoulder, which is bad news for us," Allardyce added.
"That's our third dislocated shoulder this season. I don't think I've had three dislocated shoulders in my entire career before, never mind three in one season.
"(Mohamed) Diame got only a bang on the knee where he fell on the concrete (beyond the advertising hoardings) but Joey is (out for) 10 or 12 weeks."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.