Just three days after lifting the trophy at Wembley with a dramatic victory over Manchester City, the Latics' eight-year stay in the top-flight came to an end in the pouring rain at Emirates Stadium.
Shaun Maloney briefly gave Wigan hope of another great escape as he cancelled out Lukas Podolski's opener, but three goals in eight second-half minutes from Theo Walcott, Podolski and Aaron Ramsey sealed their fate.
Martinez told Sky Sports: "I never expected this to happen. We have an incredible bunch of players at the club, they don't deserve this.
"It is a tough day for the football club. We have had an incredible eight years in the Premier League. We have to take the good things and make sure we build for the future.
"The relegation is really disappointing but it is something that we can rectify. We will bounce back as we always do as we always do at Wigan Athletic.
"The club is on a fantastic financial footing, we are stronger than ever in that respect, our football style and philosophy is something for the long term.
"I am glad that this group of players were able to show what they were capable of - to win the FA Cup is an incredible achievement.
"To win the FA Cup is an achievement that will live forever for the football club and for every individual and especially for the fans."
Wigan were guilty of some dismal defending against the Gunners, with Santi Cazorla laying on all four goals for the home side, with Martinez admitting that his side had been crippled by the injuries they sustained in defence this season.
He added: "We conceded far too many goals. Going forward we have been magnificent, but the amount of injuries that we have had in the backline is something I have never seen before.
"When you have four, five or six players missing from that position, when you keep making changes in the backline, the partnerships suffer and you concede so many goals it costs you points without playing badly."