After the full-time whistle, the Italian head coach raced down the tunnel without the customary post-match handshake with Hughes, which riled the former Wales and Manchester City manager.
Hughes told Sky Sports News after the game: "I think he just forgot for a brief moment what we do over here, win, lose or draw. In fairness he's come and apologised. I think maybe he was told to.
"It is something maybe the foreign managers don't always do and they need reminding it is something we do over here. Mind you, British managers are in a minority these days so maybe we shouldn't expect it.
"It was an emotional game and I think he was a bit emotional afterwards. He needed to be reminded, and I've shaken hands with him since."
The result sees Stoke edge up to 10th place in the Premier League table.