The Black Cats appeared to be heading towards a credible point against the in-form Toffees as Fabio Borini, on loan from Liverpool, came closest to beating Tim Howard.
To keep a clean sheet in those circumstances was very pleasing
However, former Manchester United defender Wes Brown deflected the ball past his own goalkeeper Vito Mannone from a Gerard Deulofeu cross 15 minute from time.
Everton hoisted themselves about rivals Arsenal and into fourth following their victory at the Stadium of Light, and Martinez admitted he was satisfied with the performance.
“It was a difficult game and you could tell what was at stake for both teams,” Martinez told BBC Sport.
“From our point of view, to keep a clean sheet in those circumstances was very pleasing and it was also important to take one of our chances too. It makes for a very satisfying performance full of character and personality.
“We came into this game on the back of a stylish win at home to Arsenal but in this league you have to adapt quickly to playing different teams and doing what you have to do.”
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