The Canaries were humiliated 7-0 by rampant City at the Etihad Stadium, a result that left them in the bottom three of the Barclays Premier League and increased the pressure on boss Chris Hughton.
The Norfolk side have collected just eight points from their first 10 league games and Hughton, along with Fulham's Martin Jol, is favourite to be the next top-flight manager out of work.
Martin said: "It hurts - simple as that. It's humiliating.
"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."
Norwich host West Ham in their next fixture and will need to start better than they did at Eastlands.
Samir Nasri had already hit the post when Sergio Aguero's 16th-minute shot was blocked by Michael Turner and then looped in for the opening goal off Bradley Johnson.
David Silva, Matija Nastasic and Alvaro Negredo all got on to the scoresheet before half-time in what proved a horror show for visiting goalkeeper John Ruddy.
With Joe Hart dropped by the hosts, Ruddy might have hoped to press his England claims but it proved an afternoon to forget.
Even so, he still produced three good saves in the second half to avoid even greater damage and could do little about Yaya Toure's sublime free-kick for City's fifth.
Aguero volleyed in the sixth from a poor Sebastien Bassong clearance and Edin Dzeko rounded off the scoring.
Scotland international Martin, 27, said: "I just don't know where that performance has come from, because even though we haven't been picking up results lately we've been playing okay in bits and bobs.
"The whole team just weren't good enough from start to finish.
"We had a little bit of misfortune with the first two goals but after that we totally capitulated and that's not like us."