Makeshift centre-forward Joe Aribo put the Rangers fans in dreamland when he slotted home following a slip in the German side’s defence in the 57th minute.
Frankfurt levelled 12 minutes later when Rafael Borre knocked the ball home from close range following a low cross.
Gers finished extra-time strongly and Ryan Kent was brilliantly denied at close range before Steven Davis had a shot cleared off the line, while James Tavernier had a free-kick saved in stoppage-time of the 1-1 draw.
Aaron Ramsey, a 117th-minute substitute, saw his spot-kick saved and Borre netted to seal a 5-4 shootout win.
Follow reaction from the Europa League final below: