The Scotland midfielder was involved in a heated exchange with some home supporters in the City Stand towards the end of the first half during Tuesday night's goalless draw against Newcastle, when both sides finished with 10 men following the double sending off of Loic Remy and Bradley Johnson.
Snodgrass later made a point of signalling an apology when he tracked back down the flank towards the same section of Canaries fans during the second half.
Indeed, the winger almost snatched what would have been a somewhat fortunate victory when his close-range header was scrambled away by goalkeeper Tim Krul in the dying moments of a match which had earlier seen Newcastle denied by the woodwork on three separate occasions.
Martin, 28, understands the frustrations of both those in the stands and the players on the pitch as Chris Hughton's men struggle for consistency to pull themselves clear of the relegation zone.
"It was the whole stadium. I felt it, the fans were getting tense," Martin said on Canaries Player.
"Sometimes it is hard for players, especially for Snods, who is on free-kicks and corners, for him to be bang on the money all of the time is tough.
"I feel for him because if it is not on the money, then people do criticise him.
"Snods is a winner, he really cares and is a great lad. Sometimes that frustration does boil over, he gets angry.
"Sometimes it can overstep the mark of what people want to see, but it is an intense game and there is a lot of pressure on things, passions are high and people find it difficult to control themselves.
"He means nothing by it, he has apologised at the end and I felt for him when there were a few sarcastic cheers as he put a cross over for a corner and that is not doing anyone any good.
"But the fans were chanting his name at the end, they were great, he apologised and we move on.
"As a football club we are well known for sticking together, the managers, fans and players, so nothing is going to change there."
Canaries boss Hughton was made aware of the incident, and is set to gather some more information before deciding on whether any internal disciplinary measures are needed.
Norwich really should have been made to pay for a poor first half display when they had no answer to Newcastle's interchange in a group looking to start life without Paris St Germain-bound Yohan Cabaye.
Remy's close-range shot was saved by John Ruddy, before Norwich midfielder Johnson kicked a cross onto the post.
France forward Remy then hit the outside of the other upright, before his second half free-kick crashed against the crossbar.
Norwich eventually improved in the final 20 minutes as Krul tipped a close-range shot from Gary Hooper up onto the woodwork before then blocking Snodgrass' header at the death.
"We knew we did not play the best and got away with it at half-time, but the positive you take out of it is that it is a clean sheet and could be a big point for us," said Martin.
While Norwich continue to look over their shoulders, Newcastle manager Alan Pardew hopes his side can press on in their long-term quest to secure Champions League football once again.
"It was one of those nights where their goal was charmed. We had chance after chance come, but I am very pleased with the performance because we were outstanding," Pardew told nufcTV.