Mourinho and Hughes were involved in a heated exchange on the touchline in the closing stages at the bet365 Stadium and tensions were still simmering at full-time.
United had blown a 2-1 lead as Eric Maxim Choupo-Moting's equaliser ended the Premier League leaders' 100 percent start to the season.
And Mourinho pointedly refused to acknowledge Hughes when the former United star went to shake hands at the final whistle.
Hughes responded with a mocking wave towards Mourinho, who did shake hands with members of Stoke's backroom staff.
Mourinho made it clear he didn't feel he was the guilty party.
"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," he said.
Hughes was confused by Mourinho's behaviour, adding: "I seem to get involved in handshake 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!"