The Canaries, who chose to promote Under-18s coach Adams, have slumped to just five points above the relegation zone with as many games left to play.
"It's a decision we have to accept obviously," Martin told Norwich City TV. "There's always a tinge of disappointment when a manager is relieved of his duties because ultimately it means we haven't performed enough for them.
"But we're now fully behind Neil Adams. It's an exciting appointment for the club. We're looking forward to it and getting right behind him as we go into a big game on Saturday and looking to win the game."
Norwich will travel to fellow struggling side Fulham on Saturday.