The Toffees suffered their first Premier League home defeat of 2013 on Boxing Day as the bottom-placed Black Cats pulled off a major shock.
When Leon Osman miscontrolled a short pass from Tim Howard near his own area on 23 minutes, Ki Sung-Yueng seized on the error and took the ball round the American, only to be brought down. Referee Lee Probert sent off the Everton goalkeeper and, after substitute Joel Robles had replaced Osman, Ki struck home the penalty.
That proved to be the only goal of the game, as Vito Mannone and the Sunderland defence repelled a second-half onslaught from the hosts.
When asked about the penalty incident, Martinez told Sky Sports: "It's the law of the game. It's a clear opportunity to score and that's a red card. That's probably something to debate, if that rule could be changed or not - it's a double punishment, losing a player and giving away a penalty - but we've got no complaints about it. We made a wrong decision, and it cost us.
"But I thought the second-half performance was exactly what we needed. The scoreline doesn't reflect what happened in the game, but today I'm happier probably than on other days when we won because we learned a lot from our squad and internally, and that's going to help us for the future."
It was put to Martinez that Everton's desire to play short passes at the back might have been a factor, but the Spaniard added: "It doesn't need to happen. It's one thing to play in a certain way, but a style shouldn't bring risks. Making good decisions is important.
"There is always a transitional period in whatever you want to do. You need to develop experience, and we'll learn from it. Today, that incident because of the sending-off, put a major difficulty in the rest of the game, but when you look at the amount of chances and the performance of Mannone, he had two outstanding saves and we should have taken advantage of a couple of other good opportunities.
"I couldn't be prouder. We played with 10 men; in the second half, we were always a real threat, we worked extremely hard, and I thought tactically we coped with whatever was needed. The normal thing would have been to get something out of the game, but as it happens I'm extremely happy with the performance."
Martinez insists Everton will take a great deal from the game, even if it produced no points on this occasion.
"Sometimes you can nick a win that isn't going to help you in the next five months of the competition," he added. "This performance isn't leaving us any points today, but it's leaving us a lot of future points - there's no doubt about that.
"I couldn't be prouder or happier, with the amount of desire that we showed, and on another day, we could have won. Sometimes football brings those sort of moments - and we have to learn from it."