Roberto Martínez digested the "lowest of lows" as he watched his Wigan Athletic team relegated from the Premier League following a 4-1 loss at Arsenal – and was then unable to say whether he would lead the fightback in the Championship.

The manager has been heavily linked with the post at Everton, which is soon to be vacated by the Manchester United-bound David Moyes, but Martínez's emotions were overtaken by the "heartbreak" of his club losing their eight-year grip on top-flight status. The relegation came just four days after their FA Cup final victory over Manchester City.

"This is not the time to discuss individuals," Martínez said. "We will review everything at the end of the season. If I am honest with you, it is just too fresh. I never, ever expected us to get relegated so I don't think it is the moment. We have to get ready for the final game of the season. Then, as always happens at the end of the season, there will be an assessment and whatever happens, happens."

Martínez summoned fighting talk from the depths of the despair. "The relegation is really disappointing but it's something we can rectify," he said. "We have to make sure we get stronger. We'll bounce back, as we always do, Wigan-style. The club is on a fantastic financial footing. We have huge assets. The football philosophy is there for the long term."

But he returned over and over to the theme of shock. "I can't quite believe it," he said, while denying that the FA Cup heroics had taken a toll in the league. "I know from the outside relegation was a possibility, but I never thought it would happen. We had to win the last two games but I was very confident this team could do that. It is difficult to describe my feelings because even now it is a shock. We are not a team that deserves to be in the bottom three.

"The FA Cup has really helped to give us that little bit of direction and confidence in the league. It is an achievement that we will never lose. It is just a shame we have won it in the same season that we lost our Premier League status. If you look at the history, it has never happened before. No team has been good enough to win the FA Cup and not stay up. That is why it is so difficult to take what has happened."

Arsène Wenger, the Arsenal manager, predicted that Wigan would "certainly come up again if they stay together" but his focus is now on Sunday's game at Newcastle United, in which victory will bring Champions League qualification for his team. He also reported that the midfielder Mikel Arteta was a "massive doubt" after injuring a calf.

"I am confident because we have experience," Wenger said. "We play for a long time under massive pressure and we always found the solutions to the problems we have faced. We need to win and I am confident we will."