The American goalkeeper was sent off in the 23rd minute of the Toffees' home clash with Sunderland which ended in a 1-0 win to the visitors.
The goal came from the penalty spot courtesy of Ki Sung-yueng as a direct result of Howard's decision to bring down the South Korean when he attempted to round the gloveman.
After the match, Martinez felt his side did well to continue playing in an attacking manner in the second half and was not using Howard's sending off as an excuse for just their second defeat of the season.
"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," he told Sky Sports.
"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."
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