Ireland went behind thanks to Martin Odegaard's opener but a brilliant Jake Mulraney effort levelled the tie before the break. Ireland held out until the final minute of the game but Iver Fossen's strike won the game for the home side.
With temperatures as low as minus three on the 3G surface at the Marienlyst Stadion in Dremmen, Norway dominated the early stages of the game and went ahead just before the 20th minute. A neat interchange saw Henrik Bjordal break down the left side and cut back to find Odegaard, who evaded the on-rushing Kieran O'Hara to tuck home.
Ireland responded well to going behind and just before the half-hour, Ireland saw a penalty claim turned down. Neat passing play found QPR forward Ryan Manning on the edge of the area and his through-ball found Harry Charsley who went down under the challenge of Kristoffer Ajer, but the referee waved the claims away.
Soon after, Ireland were level. Declan Rice found the run of Jake Mulraney just over the half-way line and his pace saw him fly past Julian Ryerson, and into the area to finish under the keeper in the 32nd minute.
Ireland continued to create problems for Norway during the second-half as Manning and Ronan Curtis saw long-range efforts go wide from distance. Keeper O'Hara denied Odegaard with a brilliant save from a 20-yard free-kick as the game headed towards a draw.
However, Ireland were denied a deserved point in the final minute of the match as Curtis' header only half-cleared a right-sided corner and captain Fossem fired home to give the home side all three points.
Republic of Ireland U21 Head Coach Noel King said: "It's a tough one to take. We've worked so hard throughout the entire match and we definitely deserved a point.
"To lose it in the final minute of the game, it's always going to hurt but I'm incredibly proud of this great group of players. They've shown a lot of hunger, desire and passion for the cause tonight in difficult conditions and they should be proud of their efforts.
"That is a good Norway team, full of talent, and over two games, only the final minute of the game separates us. The players are in the dressing room but they want to get into the next game against Azerbaijan next year and get another positive result on the board.
"We've had a great start to the campaign so I'm sure we'll bounce back from this defeat. It's a long campaign and I believe in this group of players."
Republic of Ireland: O'Hara (GK), Kane, Donnellan, Sweeney, Whelan, Rice, Cullen (C), Charsley, Curtis, Manning (Ronan 85), Mulraney.
Norway: Bratveit (GK), Ryerson, Hanche-Olsen, Ajer, Jenssen, Fossum (C), Thorsby, Risa (Ingebrigtsen 85), Odegaard, Reitan (Johnsen 70), Bjordal (Espejord 73)
Referee: Ville Nevalainen (FIN)