The Midlanders came from behind at Carrow Road to win 4-1, with three of the visitors' goals coming in the final 12 minutes.
Steve Morison fired the Canaries ahead on 19 minutes, with Brett Holman levelling matters just two minutes later.
And that was the way it remained until Andreas Weimann hit the target twice in the space of six minutes, and Christian Benteke completed the scoring in added time.
Villa move through to the semi-finals of the competition and Hughton admitted: "We needed to make sure we held onto our 1-0 lead longer.
"And then, at the start of the second half, we had a great chance and if that goes in then possibly it is a different story.
"Villa are a good footballing side and they were more clinical than us. It is really disappointing because we had been on a good run.
"We have to take it on the chin and now need to make sure we can get back on track for Saturday against Wigan."