The Potters manager was speaking to the press in the wake of his team’s 3-1 defeat at the Emirates Stadium on Saturday but things soon turned sour.
When asked for his thoughts on the Stoke fans’ chants, Hughes replied: “Did they? Ok, well I didn’t hear them”. At that point, the manager abruptly left while refusing to answer any further questions.
Ramsey, who was not named in Saturday's match-day squad, suffered a broken leg in February 2010 following Ryan Shawcross’ dangerous challenge on the player during a Premier League encounter between Arsenal and Stoke.
The Welshman was subsequently ruled out of the game for 10 months and reportedly refused to later accept Shawcross’ apology.
As a result, Stoke fans have since sung abusive chants at the midfielder during almost every fixture between the two teams.
Before walking out of his press conference, Hughes had confessed that Arsenal were the better side.
"We stumbled today but we have been on a good run," Hughes said.
"On another day you never know with the chances we created; we might have got a positive result. But it's fair to say they were the better side.
"I thought we did OK for most parts of the game, especially in the first half when we caused them a number of problems."
He added: "Once you go behind to Arsenal it becomes more difficult because you chase the game and they are quite adept at countering.
"We kept going and had chances, it could have gone our way but they are a very good side and lots of teams lately have struggled to keep them at bay.
"I thought we did OK in that regard and maybe the three goals is a bit harsh on us."
After falling behind as a result of Charlie Adams’ 29th minute penalty, Arsenal soon hit back and went on to secure a 3-1 victory courtesy of goals from Theo Walcott, Mesut Ozil and Alex Iwobi.
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