Everton saw their FA Cup dreams ended by three second-half goals as Arsenal booked their place in the semi-finals and a trip to Wembley.
Romelu Lukaku cancelled out Mesut Ozil's early opener, but Mikel Arteta's penalty and substitute Olivier Giroud's quick-fire brace in the last seven minutes put the game beyond the visitors.
Martinez felt the scoreline was harsh on his side as they gave as good as they got for long periods of the game.
"It's hard to take but we lost a tie giving everything and trying to win," said Martinez.
"The scoreline at the end doesn't reflect what happened in the game. It shows what we have in the dressing room, trying to go forward right until the final whistle.
"We weren't happy with the first goal and we need to be much better with our defensive duties. But once we steadied ourselves after the first 20 minutes we were where we wanted to be.
"Unfortunately, we couldn't score that second goal to put the game in our favour."
Martinez felt two key incidents swung the game towards Arsenal, with Arteta scoring from the penalty spot after Ross Barkley fired over a good chance for Everton.
"I felt it was a situation where Gareth (Barry) was fighting for the ball with Oxlade-Chamberlain," added Martinez. "Of course there was contact but was there enough contact to give a penalty?
"They are difficult decisions and you need luck to be in your favour. Then, from our point of view, there was the chance before that.
"We wanted to make it an open game and have the opportunities to score the second goal. Nine out of 10 times Ross always hits the target from those positions."