The pair clashed towards the end of Saturday's 2-2 draw between the two sides, with Hughes appearing to push Mourinho as the Portuguese encroached on the Welshman's technical area.
The situation then appeared to have calmed, only for the two coaches to head straight down the tunnel without shaking hands at full time.
Speaking after the game, Hughes confirmed that he pushed Mourinho, saying: 'I pushed him because he was in my technical area. Maybe that is why he didn't want to shake my hand. It has to be viewed as a negative result for him.
'Maybe he reacted in the wrong way. In fairness I have my history with handshakes. Maybe it's me.'
When asked about the incident, Mourinho told the 'BBC': 'I prefer not to answer the question, because it looks like it is my fault and that is not correct.'
Whilst in his interview with 'BT Sport' the Manchester United boss was somewhat more blunt. 'I don't speak about stupid things, I'm too old for that, talking about stupid things is for stupid people,' he stated.