The result ended a run of three league games without a win for Martinez's side and lifted them to ninth in the table, a point and a place behind Merseyside rivals Liverpool.
"They (Stoke) are a team that have some very important players with a lot of flair and creativity," Martinez told the club's website (www.evertonfc.com).
"We know how tough they can be. We faced them last season in a really competitive game (a 2-0 win for Stoke in March) and I expect exactly the same.
"They have already shown that on their day they can beat anyone. Stoke were very impressive against Manchester City not so long ago."
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Stoke have beaten both the Manchester teams in the league this season, becoming only the second team to have done so after Arsenal.
Martinez also said Monday's game would provide a pointer to how his team would fare in the second half of the season.
"After the game, we can look forward to the second half of the campaign knowing every single team, and knowing where we sit in terms of the quality of our side compared to others," he added.
(Reporting by Nayan Das in Bengaluru; Editing by John O'Brien)
