Conference side Wrexham were facing a side 96 places above them in the Football League structure and were all set for a famous cup upset when Mark Carrington headed home a 73rd-minute opener at the Britannia Stadium.
Stoke showed their Premier League class in the closing stages, though, and turned the match on its head thanks to Marko Arnautovic's 80th-minute equaliser and a late double from substitute Stephen Ireland.
Manager Hughes, who hails from Wrexham, was unhappy that his team failed to show their best form on their way to round four.
"I'm just pleased we are in the hat for the next round, to be perfectly honest with you, because Wrexham deserved a replay from that," Hughes told Stoke's official website.
"We didn't play anywhere near the levels that we expected to and fair play to Wrexham because they were fantastic throughout the game.
"They worked exceptionally hard, chased lost causes and were thoroughly deserving of the lead that they had at the time.
"Thankfully we were able to get back on level terms and Stephen Ireland came on and gave us the craft that we had been missing for the vast majority of the game.
"All in all, we are happy to still be in the competition, but we know we have to perform far better than that if we are to continue progressing, which is what we are aiming to do."
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