Hughes and Mourinho clashed during the match when Mourinho strayed into his opposite number's technical area, and the Portuguese boss was quick to turn away from the former United striker at the final whistle.
The Welshman admitted that he was unsure about Mourinho's reason for the snub, but was pleased with his side's display and reserved special praise for stand-in skipper Darren Fletcher and two-goal Eric Maxim Choupo-Moting.
"[The handshake] didn't happen. 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," he told BBC Sport.
"[Choupo-Moting] will get the headlines and rightly so because he was a big part of the performance and the result overall. He should be pleased and I was delighted when I got him here. It was a decent bit of business in my view.
"[Fletcher] has come to us and I haven't been disappointed in any aspect. He has had to overcome adversity with his health and you can see how that has shaped his career. We were missing our captain but he stepped up and you can see the qualities he possess in terms of leadership.
"We were up against the best side in the Premier League judging by what they have shown so far. We didn't allow them as much space and everything I asked the guys to do, they fulfilled. We have had a tough start. We are showing the potential we have and we look in good knick and we're all excited by what is ahead for us."
Stoke have now picked up four points from two home games against Arsenal and Manchester United this season.