Marcus Rashford and Romelu Lukaku scored for United, while Maxim Choupo-Moting netted twice for the hosts at the bet365 Stadium.
Hughes offered his hand at full-time but Mourinho declined the offer. He however shook hands with Hughes’ backroom staff.
This came after the two men had argued on the touchline as their teams did battle on the field.
Fans on Twitter claimed Hughes told Mourinho to “f*** off” at one point.
“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.
“I don’t get involved with stupid things like this, I am too old. Stupid people talk about these things,” Mourinho said.
Hughes added: “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!”