The Merseyside club had a right to feel aggrieved after De Bruyne turned in Raheem Sterling's cross to level the aggregate scores at 3-3 as replays showed the ball had gone out of play in the lead-up to the goal.
"The decision is tough to take," Martinez told reporters after the game.
"But as a football club we need to see the signs that, if we all push together and if we're all patient enough, we'll get the rewards and make sure that one day we look back on this moment, this hurt and say it made us fulfil the potential that we have in that dressing room."
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This was not the first time this season an officiating error has cost Everton dear.
John Terry's last-minute equaliser for Chelsea in the 3-3 Premier League draw earlier this month was also allowed to stand, despite replays suggesting he was offside.
Everton still have a chance of reaching Wembley this season in the FA Cup and can take another step in that direction in their fourth round tie against fourth tier Carlisle United this weekend.
"There have been a few big decisions go against us lately, but then it should give us inspiration to pay our fans back by getting them to Wembley this season," said the Spaniard. "We still want to make our season count."
(Reporting by Shravanth Vijayakumar in Bengaluru)
