Chris Hughton's men now reside in the relegation zone after their Eastlands humbling, which was their sixth league defeat of the campaign and biggest ever in the top flight.
As well as shipping 20 goals in 10 matches, City have only scored six, and Martin conceded that Saturday's heavy loss would be a test of character for his side, with West Ham the visitors to Carrow Road this weekend.
"Let's see what we're really made of now," Martin said.
"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."
