Last season's Europa League finalists Ajax went out in the qualifying rounds as Rosenborg beat them to reach the group stage.
The Dutch giants trailed 2-0 on aggregate when Nicklas Bendtner scored.
But they led on away goals after Amin Younes and Lasse Schone both scored in the space of two second-half minutes.
However, Samuel Adegbenro - who also fired home in the first leg - netted twice in the last 10 minutes to send the Norwegians through.
Ajax, who lost to Nice on away goals in their Champions League qualifier earlier this summer, have failed to win a European game in a season for the first time since 1990-91, when they did not compete.
AC Milan beat Shkendija of Macedonia 1-0 to complete a 7-0 aggregate win and qualify for the group stage after three years out of European competition.
Marseille went through 4-1 on aggregate after a 3-0 home win over Slovenians Domzale.
Athletic Bilbao are also in the groups, after beating Panathinaikos 1-0 and 4-2 overall.
Vardar became the first Macedonian side to reach the group stage of a European competition after a 2-1 win at Fenerbahce, secured a 4-1 aggregate victory.
Line-ups
Rosenborg
Formation 4-3-3
- 1Hansen
- 21MidtsjøBooked at 21mins
- 14Bjørdal
- 16Skjelvik
- 3MelingBooked at 48mins
- 7Jensen
- 25LundemoSubstituted forVilhjálmssonat 58'minutes
- 8Konradsen
- 26JevtovicSubstituted forAdegbenroat 68'minutesBooked at 90mins
- 9Bendtner
- 11de Lanlay
Substitutes
- 4Reginiussen
- 5Rasmussen
- 10Vilhjálmsson
- 17Levi
- 20Gersbach
- 24Østbø
- 28Adegbenro
Ajax
Formation 4-3-3
- 1Onana
- 3VeltmanBooked at 87mins
- 4de Ligt
- 26ViergeverBooked at 45mins
- 35Dijks
- 6van de BeekSubstituted forHuntelaarat 45'minutes
- 20Schöne
- 10Ziyech
- 45KluivertSubstituted forCernyat 38'minutes
- 25DolbergSubstituted forZeefuikat 78'minutes
- 11Younes
Substitutes
- 9Huntelaar
- 15Eiting
- 17Cerny
- 21F de Jong
- 22van Leer
- 37Dankerlui
- 42Zeefuik
- Referee:
- Ruddy Buquet
- Attendance:
- 21,211
Match Stats
- Possession
- Home38%
- Away62%
- Shots
- Home9
- Away17
- Shots on Target
- Home3
- Away8
- Corners
- Home4
- Away11
- Fouls
- Home3
- Away14