The Toffees boss saw his charges lose their unbeaten home record in the top flight this year thanks to a Ki Sung-Yueng penalty after 25 minutes at Goodison Park.
Goalkeeper Tim Howard's dismissal for a foul on the Swansea City loanee in the lead-up to the spot-kick ensured Everton went down to 10 men and they were ultimately unable to find a way back into the contest.
However, Martinez had nothing but praise after his side threw all they had at a stubborn Sunderland defence.
"We made a bad decision, which cost us a sending-off and a goal and that changed the game completely," he told reporters.
"It would be easy for me to say that was the reason we lost the game but I thought the second half performance was excellent," he said.
"I've learned a lot from our second half performance. I thought we were terrific after half-time and deserved an equaliser.
"If we had got the equaliser, I have no doubts we would have won the game. We didn’t get any points today but performances like that will get us positive results over the season.
"I do feel that after that performance we are stronger than we were before the game."
The result leaves Everton fifth in the Premier League table with 34 points, five points off leaders Arsenal.