The visitors frustrated Everton for most of the first half before Gerard Deulofeu broke the deadlock right on the stroke of half-time and things got worse for Stoke when Seamus Coleman doubled the advantage four minutes into the second half.
Everton completed the rout with further goals from Bryan Oviedo and Romelu Lukaku, and Hughes had no complaints with the defeat after admitting Everton deserved the win.
Asked what the turning point of the game was, Hughes told Sky Sports: "Well, from our point of view probably either side of the half-time break because we were, I think, something like 30 seconds from the half-time whistle.
"If we had gone in at 0-0, I am not saying it would have changed the result, but certainly the scoreline would have been different.
"I felt we were still very much in the game but we conceded a poor goal right on the stroke of half-time which you talk about before the game about key moments and key periods in games, and either side of the half is obviously the key moment, and we conceded two goals in that period either side of it.
"So at 2-0 down you can either accept you are going to get beaten or actually try and get something out of the game which we did with a few changes and tried to chase the game but in the end that hurt us more than obviously trying to keep it a little bit tighter and seeing what happens.
"All in all the two goals either side of half-time was the key from our point of view.
"But in fairness Everton were better today.
"I don't think it would have changed the result if we would have defended better in that half-time period because I think Everton deserved to win on their performance."