The Canaries club captain had hoped his team-mates would show their mettle against City, but the visitors never competed at the Etihad Stadium.
Chris Hughton's side are still in the bottom three, having collected just eight points from their first 10 Premier League games this season.
Martin admits the result was hard to take, and the Scotland international is determined to turn the situation around as quickly as possible to ease the growing pressure on boss Hughton - starting with Saturday's visit of West Ham.
"It hurts - simple as that. It's humiliating," Martin said. "We've let ourselves down and we've let the manager down.
"There is going to be a lot of soul-searching and conversation about this game, analysing it and going through it. We will see what we are made of now for next week.
"We have got the characters in the dressing room. It is a good dressing room, a confident dressing room. We believe we are good enough to be in this league.
"Next week we will see what we are really made of."