The Canaries saw a forgettable season hit a new low in their last Premier League outing, as they were hammered 7-0 at Manchester City.
A response is now being demanded to that hapless showing, with just eight points collected from 10 outings this term.
That return has Norwich languishing inside the drop zone, and Martin admits the time has come for their true colours to be displayed.
He told the Pink'Un ahead of a weekend meeting with the Hammers, who are just two points better off at present: "Let's see what we're really made of now.
"I know we've got good enough characters in the dressing room to deal with this and get through this. We'll see on Saturday and that will be the ultimate test, how we respond in front of our own fans.
"West Ham can't come quick enough. Man City is going to hurt for a long time but you have to move on in football quickly.
"You have to take the next game as it comes. It's West Ham at home. It's a big one for us, it was always going to be a big one for us, because home games are in this league. So it's up to us to make sure we put in a performance and get a result."
Martin also says that manager Chris Hughton - who has seen his position called into question of late - retains the full backing of the Carrow Road dressing room.
He added: "We're all behind the gaffer and that still remains the same. We weren't good enough on Saturday and he'll get a lot of stick for that, and so will we, and rightly so.
"I'm sure we're going to take it in the neck all week, until the next game when we'll hopefully put it right, but we deserve what we get."
Watch Norwich v West Ham live on Sky Sports 1HD from 5pm on Saturday.