Everton dominated the game from the outset at Goodison Park, but looked set to go in level at the interval after struggling to break down Stoke's resolute defence.
However, the outstanding Gerard Deulofeu finally put the hosts ahead after a well-crafted team move on the stroke of half-time, before Seamus Coleman doubled their lead in the 49th minute.
Bryan Oviedo and Romelu Lukaku then rounded off Everton's convincing victory with goals three and four, but Hughes was in no doubt as to where and when the game was lost for his side.
"Up to just before the half-time whistle, we’re very much in the game, so to concede right on the whistle is disappointing," the Welshman said.
"And lo and behold, we come out (after half-time) and concede within two minutes. Two goals either side of half-time really shaped the game in a negative way (for us)."
Stoke failed to get a foothold in the game as they struggled to contain an energetic Everton outfit, and Hughes admitted the better team won.
"We were poor on the day in fairness but credit to Everton, I thought they were very good and made it really difficult for us," the former Manchester City boss added.
"The movement and the pace they have was a little bit too much for us … we had too many (players) not quite at the level they needed to be. We take our medicine and move on."
