Former Rangers striker Cyriel Dessers scored twice, including a 125th-minute penalty, to send Panathinaikos through in Europe.
Derek McInnes was left without a match-winner as Rangers crashed out of the Conference League after 120 minutes in Jablonec, Czechia.
Ryan Naderi, Lawrence Shankland and Bojan Miovski could not find the breakthrough Rangers needed.
Rangers’ European campaign ended with defeat, while Dessers made the difference for Panathinaikos in Hradec Kralove.
The Greek side had drawn 2-2 with Viktoria Plzen in the first leg, when Dessers came off the bench. He started the return match among the substitutes before entering on the hour mark.
The Nigerian international needed only 12 minutes to make an impact, firing Panathinaikos ahead. That goal appeared to settle the tie, but Vladimir Darida scored in the 92nd minute to force extra-time.
Dessers was then given another chance to decide the match in its closing seconds. Panathinaikos were awarded a penalty in the 125th minute, and the 31-year-old converted before celebrating with his team-mates in front of travelling support.
The result sent Panathinaikos into the Conference League league phase.
Rangers, meanwhile, were left to reflect on a night when they could not produce a chance or finish in front of goal.
Dessers left Ibrox for Panathinaikos last summer after playing for Rangers against the club in Champions League qualifying.
His first season in Greece was disrupted by injury, limiting him to eight appearances in competitions. He scored three goals and provided one assist.
He has started the campaign with three goals in three matches. His double came as McInnes lacked a clinical option to rescue Rangers’ European campaign.
