It was always going to be a big ask for Wigan to lift themselves for such a huge game just 72 hours after their glorious Wembley victory over Manchester City, where anything other than all three points would have seen them join Reading and QPR in the npower Championship, and so it proved.
Lukas Podolski nodded the Gunners in front on 11 minutes, but Shaun Maloney gave the visitors hope when he crashed home a free-kick on the stroke of half-time.
However, three goals in the space of 10 minutes just after the hour from Theo Walcott, Podolski and Aaron Ramsey meant there was to be no fairytale ending for Martinez's men, despite another brave crack at the great escape.
"I know from the outside you could see it was possible but I never thought for a second it would happen," said the Spaniard, who has been linked with the Everton job following the announcement of David Moyes' switch to Manchester United.
"I was confident this team could win the last two games. It is difficult to describe the feelings. It comes as a shock.
"I don't think you get many managers saying they are proud of their players when they get relegated, but we don't deserve to be in the bottom three.
"You will never see a better group of players than these in the way they play and represent the club."
Martinez added: "The FA Cup is an achievement we will never lose as a club. It is our first silverware, but it is a real shame it happens in the same season as relegation.
"You don't normally get teams good enough to win the cup going down - that is why it is difficult to take.
"When you walk into the dressing room after this match it is heartbreaking.
"But we haven't been good enough in the defensive area and that is why we have been relegated."
Martinez, however, insisted the Lancashire club, whose rise to the top flight was bankrolled by chairman Dave Whelan, would be in a strong position to make a swift return.
"It is not one of those moments to be too sad - it is the opposite," he said.
"To have eight years at this level is incredible. We have beaten every top club and financially we are in a strong position. As a Wigan fan it is a time to be proud of what we have achieved."
Wigan have several players who are bound to attract the attention of top-flight clubs, with Callum McManaman being named in the England Under-21 squad for next month's European Championships.
Martinez said: "In the summer, as always happens, there will be assessments and whatever happens will happen.
"Every football club in the world will lose players. There is a price and when you get that you have to reinvest in good players - that is not a worry at all.
"We don't have to balance books - we are not going to lose players on the cheap. Everything is on a good financial structure - even in the Championship."