Adams has stepped into the role from his position with the youth team, after the club dismissed Chris Hughton and his assistants Colin Calderwood and Paul Trollope on Sunday.
Norwich have been flirting with relegation in recent months, and Saturdays 1-0 defeat to fellow strugglers West Brom forced the club to axe the coaching staff with five Premier League matches remaining.
Martin is confident Adams will settle quickly after his promotion, and he reckons the team will respond.
"I think a lot of the squad watched a lot of the Youth Cup games last year and saw how well he done with the players there," he said.
"I'm probably aware of Neil a bit more than some of the lads because of the length of time I've been here. He sees us playing every week.
"He's going to know our strengths and weaknesses as players but as characters and personalities probably not, so he's going to have to try and get that quickly.
"You've got lads who haven't been playing under previous management, they'll be desperate to impress now. That's the same if a manager was coming in from outside.
"So nothing changes there. Someone comes in, hopefully it galvanises the boys and we'll still have that togetherness and that belief that we will be fine in this league."
And the Norwich defender revealed Hughton's sacking was unexpected among the players.
"There was probably surprise among the squad with the timing and stuff, but the club make a decision and as players you have to accept that decision and you have to get on with it pretty quickly," he said.
"I've texted him and had a text back, so I'll speak with him when it all dies down a bit in the next couple of days. I spoke to Colin. They are good people and they were well liked by the lads, they had a lot of respect for them.
"We have to shoulder a lot of responsibility for them going as we haven't been good enough on a consistent basis."