The Canaries suffered a second home defeat in 48 hours when they lost 1-0 to a somewhat fortuitous strike from United substitute Danny Welbeck at the start of the second half.
Norwich, though, had enjoyed the better of the opening 45 minutes as they looked to get the bitter disappointment of the Boxing Day defeat by Fulham out of their system.
Full-back Martin saw his angled shot palmed away by United goalkeeper David De Gea, who also saved from Gary Hooper before Wes Hoolahan's goalbound shot was blocked by Jonny Evans.
Despite the frustrations of another fruitless afternoon's efforts, Martin believes Norwich can be positive heading into the New Year's Day trip to Crystal Palace, when Chris Hughton's men will look to again put some distance between themselves and the scrap for survival.
"It is extremely difficult to take because, if you analyse the game, they did not create too much and the goal we have given away was very poor," the Scotland international said.
"We should have had a couple ourselves, and it is a problem we have not quite got right yet because we are not scoring enough goals.
"We should have been ahead going into half-time, but weren't and always knew they would have a good spell.
"But this was a much better performance than on Boxing Day, so that is a positive and if we can reach this level of performance again and with this intensity at Palace on New Year's Day, then can go there and get a result."
Martin added: "We just need to be a bit more clinical in the final third.
"We have created quite a bit, but it has not quite fallen for us.
"It is something we know we have to sort out and put right, and hopefully it will come."
Hughton's side retain a slender three-point cushion over the bottom three, but that could be wiped out should they lose at Selhurst Park and results elsewhere go against them.
"It seems that every game that you play is a big game," said the Canaries boss said, who substituted striker Gary Hooper in the second half as a precaution against muscle tightness.
"It is very competitive in this division and there are a lot of teams round where we are and the points that we have.
"We picked up the momentum with regards to performance, but, out of the two games we have played (over Christmas), by far the bigger disappointment was two days ago against Fulham, when then the performance level wasn't anything like what we had against United and if it had have been then I am quite sure the result could have been different.
"It is disappointing that we have had two home games and not taken any points from them, but we have to take that same quality that we showed against United into Wednesday's game at Palace."