Hughes’ Stoke side came back from 2-1 down to frustrate Moutinho’s men at the bet365 Stadium.
The two managers were involved in a spat before the end of the match when Mourinho walked into Hughes’ technical area to talk to the fourth official.
The referee was called over to sort out the dispute.
But there was clearly no love lost at the end of the match as Mourinho walked away from Hughes when he offered his hand out at the final whistle.
Hughes then waved away the Portugal boss, who went over to Stoke’s bench to shake hands with the home staff.
Hughes said of the incident: "It didn't happen. I seem to get involved in hand-shake issues!
"I'm not sure why he didn't want to shake my hand, I didn't think there were any issues.
"There was a time he came into my technical box and I told him to get out but that was it. Maybe that was what upset him!"
Asked about the snub, Mourinho said: "I prefer not to answer question about handshakes - it's a bad question. It makes it look like it's my fault but that's not right."
PA
Mourinho refused Hughes' handshake at the end of the match
On the match Mourinho said: "No I'm not satisfied with a point because we were the team closer to winning.
"I have to say it is a result I accept though.
"One team tried to win, one team tried to get the point but they fought hard to get that point - they defended well, they counter-attacked and in set-pieces they are powerful."
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