The Toffees blitzed their hosts at a rain-lashed Britannia Stadium with first-half goals from Romelu Lukaku, Seamus Coleman and Aaron Lennon, and created several further chances to add to their tally after the break.
The comprehensive win came only a day or so after footage had emerged showing Martinez producing some interesting dance moves at a Jason Derulo concert.
And when asked if he had been tempted to do something similar at the end of the match, Martinez said: "I thought about it, if I'm honest with you!
"But I felt it would be difficult to beat the moves we had on the pitch.
"I think today the likes of Tom Cleverley, Ross Barkley and Romelu Lukaku had the best moves of the game. I'm going to keep mine for another occasion!"
Everton have been accused of underachieving this season, but this Premier League win strengthened the impression they are turning a corner as they moved up from 11th to eighth in the table.
It was the first time they have registered back-to-back league wins in 2015-2016, and also represented a third straight victory in all competitions, with each of them being 3-0 results.
While frequently looking potent in attack, the Toffees have also had a habit of blowing leads this term.
And Martinez said: "Overall, to come to the Britannia Stadium and get that scoreline with the controlling performance we had was very pleasing.
"I think it shows how far we have come this season and how hungry the group is to finish the season really strong.
"Being able to be mature with our performances has been a real enigma this season.
"We are a team with a big amount of goals from open play, but managing scorelines has been a real problem.
"Sometimes it has been a lack of maturity, sometimes a lack of focus.
"But I think in the last three games we have shown a real understanding of what to do on a football pitch.
"I'm looking forward to seeing how strongly we can finish the season."
Everton grabbed the lead in the 11th minute as Lukaku's penalty, awarded for Jack Butland's foul on Cleverley, took him to 20 goals for the season.
A Coleman header extended the advantage in the 28th minute, and Lennon then punished a Philipp Wollscheid error with a slotted finish in the 42nd.
Things could have got even worse in the second half for a lacklustre Stoke side, with the efforts of Butland - including tipping a Lukaku header onto the bar - key in ensuring they sustained no further damage.
The Potters, who slipped a place to 11th, have now lost three league games in a row, all 3-0, and with them also exiting both domestic cup competitions of late, their season looks in danger of fizzling out.
Boss Mark Hughes was keen after the game to highlight the positive individual performance the club's new record signing Giannelli Imbula produced on his debut, but was in sombre mood overall.
Hughes said: "It was a disappointing result and performance.
"Sometimes you just have to accept it is not going to be your day.
"It is always difficult when you are chasing the game as the home team because there is an onus on you - and rightly so. Your fans want you to try and get back into the game.
"But when you do that, there is always that risk you are going to leave yourself exposed."