Nantes deservedly progressed on aggregate, but GOG will rue their missed opportunities in the first match, which they lost by a single goal.
In the home match in Svendborg a week ago, GOG did not manage to build on an otherwise great start to the match. Instead, the victory was thrown away, and Nantes won by a single goal.
Nantes were even more superior on French soil, although GOG began Wednesday's game in promising fashion.
The GOG players remained competitive until 7-7 and enjoyed a lot of success with an effective counter phase.
However, then the French began to limit their mistakes, and the home team's goalkeeper, Ignacio Biosca, showed great form between the goalposts.
Hjalte Lykke had difficulty shooting from distance, and the GOG defender was unlucky to hit the woodwork several times.
Nantes extended a lead of 13-10 to 20-11, which basically decided the match.
The French team was in full control at the break with a 21-12 lead, and GOG had a mountain to climb.
In the second half, GOG could praise themselves lucky that the French outfit decided to rest on their laurels.
The excitement was long gone, and both teams also began to rotate their squads to give lesser-known names a chance to impress.
GOG didn't get many of its normally dangerous shooters going. Lasse Vilhelmsen had the most luck and became the away team's leading goal scorer with six goals, while Frederik Bjerre's effort was limited to three goals.
For the home team, Valero Rivera in particular sparkled with nine goals as the match's leading goal scorer.
While GOG was eliminated, Aalborg is among the tournament's quarter-finalists.