"We have taken one point off a very good Everton team and maybe before the game started we would have been happy with that," Hughes said.
"I thought in the first half we played really well, and then in the second half we came out and got a good goal from Assaidi (who joined Stoke on loan from Liverpool earlier this season and has now netted four times for the Potters). He is really playing well at the moment and showing the threat he has.
"You know at some point Everton will throw people forward, take chances and try to make something happen, but I was really happy with how we showed what was required, putting our bodies on the line and blocking shots.
"You get to within a couple of minutes of the end of the game and you expect to see it out, but we made a mistake and we ended up with only one point.
"But 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."
Hughes confirmed Potters goalkeeper Thomas Sorensen had come off at half-time due to an Achilles problem.
Stoke already have first-choice stopper Asmir Begovic out injured with a broken finger, so Jack Butland came on for his debut.
Meanwhile, Martinez has said Everton defender Sylvain Distin, who did not feature at the Britannia Stadium because of a hamstring complaint, is likely to be sidelined for 10 to 12 days.