The Potters, who took the lead in the Barclays Premier League contest through Oussama Assaidi's 49th-minute strike and were only denied victory by a stoppage-time Leighton Baines penalty, had lost the reverse fixture 4-0 at Goodison Park on November 30.
And they went into Wednesday's game having been defeated 5-1 at Newcastle and 3-0 at Tottenham in their last two matches of 2013.
Hughes was keen to highlight those other results when giving his assessment of the encounter at the Britannia Stadium, saying: "Only a few weeks ago, we were getting beaten quite comprehensively by the same team at Goodison Park, so we turned that around.
''And we have obviously had a difficult time over Christmas in terms of travelling and those results, but we have picked ourselves up and put in a really good performance in my view.''
Everton were twice inches away from taking the lead in the first half as Kevin Mirallas struck first the crossbar and then the post, before on-loan Liverpool winger Assaidi made the breakthrough for Stoke, rifling in from the edge of the box.
The Toffees piled on the pressure towards the end of the game and after Jermaine Pennant upended his fellow substitute Leon Osman in the area in the dying moments, the resulting spot-kick was swept in by Baines.
Hughes expressed his belief the 12th-placed Potters had deserved all three points for their display, but also indicated the result was, before kick-off, one he may well have been happy to take - and admitted he had no complaints about the decision to award the penalty for winger Pennant's tackle.
Hughes said: ''He (Pennant) has made a mistake - he has made a challenge in the box and in those situations you want full-backs or defensive-minded players to be in those positions.
''Unfortunately he miscalculated and it was a stonewall penalty.
''He is an attack-minded player. It is not one of his strengths, trying to stop balls into the box and opposing attacking players.''
Everton manager Roberto Martinez, whose side slipped from fourth to fifth in the table, revealed he had been feeling it was not going to be the Toffees' day.
Martinez said: ''I thought - given the conditions in terms of the wet weather and this moment in the busy Christmas period, with the squads getting really stretched - that whoever scored the first goal, that was going to be final.
''And I felt in the first half, when we hit the woodwork twice, that it was not going to be our day.
''I don't think we were at our best by any stretch of the imagination.
''But what we showed was an incredible reaction after we conceded the goal."