Giovanni van Bronckhorst's men could not have come closer to making history at the Ramon Sanchez Pizjuan on Wednesday evening.
They took the lead through Joe Aribo’s cool finish after some slapstick defending from the German side but were pegged back beg quickly as Colombian striker Rafael Santos Borre took advantage of some poor defending from Rangers as they failed to deal with a simple cross.
Rangers grew as the game went on and were arguably the better team when the game went to extra-time. They created by far the best chance to win it when substitute Kemar Roofe ran on to a long ball, hit the byline and fired a cross into the path of Ryan Kent but the winger was denied by a brilliant stop from Kevin Trapp. Steven Davis sent the rebound over the bar via a deflection.
It took the match to penalties, taken in front of the Rangers support behind one of the goals. Nine of ten spot kicks were scored. However, it was Aaron Ramsey, the big-name January signing who missed the decisive penalty, shooting down the middle, Trapp repelling the effort with his feet.
Frankfurt's penalties were all either emphatic or well placed with Allan McGregor having little chance.
Now Rangers must switch their focus to Saturday's Scottish Cup final clash with Hearts at Hampden Park.
Here is The Scotsman's ratings out of ten for all 17 players to get game time.
9. Scott Wright - 5
Was one of the team’s better players in the first half, showing some lovely touches to turn and create space. Fell out of it after the break, allowed the cross to come in for the equalising goal too easily and was hooked after a booking borne out of frustration. Photo: JAVIER SORIANO
10. Joe Aribo - 7
The scorer of a Rangers goal in a European final. He pounced on the Frankfurt mistake to calmly put his side in front. Up to then it was an erratic performance. Was coming short when Rangers needed him to go long and vice versa. But his qualities ensured he kept the defence on their toes. Influence waned when moved wide. Photo: JAVIER SORIANO
11. Ryan Kent - 5
The winger was on the periphery for large parts of the game. When he was on the ball there was a buzz and expectation that he would produce the goods but was often crowded out or sent down an alley with no return. Had two good chances but lashed at the first then was denied by an excellent save by Kevin Trapp. Photo: JAVIER SORIANO
12. Steven Davis - 7
Brought a class and elegance to the middle of the park. Played the game at his own pace and ensured Rangers finished the stronger team. Photo: JORGE GUERRERO