The Potters allowed Gerard Deulofeu to break the deadlock with 30 seconds of normal time remaining and then they were punished after the break, conceding three more to slump to a 4-0 loss.
"We were poor on the day but credit to Everton, I thought they were very good and made it difficult for us," Hughes said.
"The disappointing thing for us was up to 45 seconds prior to the half-time whistle we were very much in the game at 0-0.
"To concede right on the whistle, which is a key time in any game, is disappointing and lo and behold in the second half we came out and conceded early.
"That really shaped the game in a negative way. We tried to get back into the game but that just compounded our problems as we were a little bit over-exposed because we were trying to get back into the game.
"Four-nil was a little bit harsh on us. If we'd got to half-time at 0-0 I don't think the result would have been different but it might not have been as harsh."