City midfielder Bernardo Silva and manager Pep Guardiola were both complimentary of Saints in the aftermath.
Martin said, "Yes, as was Phil Foden. I think they felt that we were really brave with the ball and we did, like Phil said, we did some stuff to them that not many teams do. Pep congratulated us on the way the team looks and the way it plays.
"I think, yes, it's not easy to play that way and he probably understands that more than anyone. But we really believe in it. We have to believe in something and I've seen so many teams get promoted and just change and then end up nowhere.
"We've been a little bit, in between the last few weeks, not quite where we want to be because we have to be extreme in some ways. To take the ball in places people would not enjoy taking it usually. We have to play with extreme courage all the time.
"In moments when we've gone ahead, especially recently, it's been quite tense and not us. I just don't enjoy that. So if we lose, I can accept it when the lads show a level of courage like they did today.
"I hope now we can get them to live there all the time because if they can do that here, they can do that anywhere. So whilst compliments are nice and all that, it still hurts to lose. But there is a way for us to lose.
"I'm going to live and die by the sword in what I believe in. Otherwise, I just can't do it. The players really believe they're fighting. Subjectively we should be doing better. Objectively we should be doing better as well."