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Our skipper came on at half-time after we had fallen behind to an Aaron Luopalo-Bi effort, but helped force the issue as we equalised through Viktor Gyokeres.
But we couldn't make our dominance count as the game went to penalties, where we lost 5-3 on spot kicks at Highbury.
After the game, Odegaard said: "It's very frustrating to go out. Obviously, the way we’ve played was not on the level. We need to do much, much better than we did today.
"Frustrating, but congratulations to Fleetwood and we look forward to the next game already and bounce back.
"They did well so we have to give them credit, but I think today was about us not being on our level, we need to do better. I thought we improved during the game, but again, we need to step up even more - so that’s a shame."
The games are coming thick and fast, and we turn our attention to facing Liverpool at Anfield on Sunday - and the captain said there's no time to dwell on the defeat.
"We can't feel sorry for ourselves," he said.
"We need to move on - we have a big game at the weekend, so bouncing back at the weekend is all we can do now.
Lastly, Martin thanked our travelling support, saying: "Massive thanks to them again for travelling - it’s a long journey - just thank you, and sorry for the result."