Danny Welbeck's early second-half strike was the difference between the two sides as Norwich slipped to their second loss in 48 hours following their 2-1 defeat at home to Fulham on Boxing Day.
Martin bemoaned Norwich's inability to take their chances against United, but insisted their display has given them encouragement ahead of their visit to Selhurst Park on Wednesday.
"It is extremely difficult to take because, if you analyse the game, they (Manchester United) 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 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.
"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, we can go there and get a result."
Norwich are three points clear of the relegation zone but could find themselves in the bottom three if they lose to Palace and other results go against them.
Manager Chris Hughton acknowledged Wednesday's match is yet another big game for his side.
"It seems that every game that you play is a big game," Hughton said. "It is very competitive in this division and there are a lot of teams round where we are and the points that we have.
"It is disappointing that we have had two home games and not taken any points from them," he added. "But we have to take that same quality that we showed against United into Wednesday's game at Palace."