Joe Aribo had the Gers fans in raptures in the searing heat of the Ramon Sanchez-Pizjuan stadium when he opened the scoring in the 57th minute.
However, Colombia forward Rafael Borre levelled in the 68th minute to give the game 30 added minutes where Frankfurt goalkeeper Kevin Trapp made a fantastic last-gasp save from Ryan Kent.
Then came penalties and despair for the Light Blues and substitute Aaron Ramsey in particular who had his spot-kick saved.
The match finished in heartbreak for the Premiership team.
Rangers in Seville: Latest updates and news ahead of Europa League final | TV Details | Rangers v Eintracht Frankfurt TV details
Last updated: Thursday, 19 May, 2022, 12:08
In the third qualifying round, Sturm Graz and Union Saint-Gilloise are possible opponents.
Dynamo Kyiv and PSV Eindhoven could be opponents in the play-off round.
What does defeat mean for Rangers?
Former Rangers manager Ally McCoist hailed the team’s “great achievement” in reaching the Europa League final following the “cruellest” of defeats.
McCoist caught sight of his children feeling the pain in the crowd after Rangers lost on penalties to Eintracht Frankfurt following a 1-1 draw in Seville.
McCoist told BT Sport: “It’s heart-breaking, that’s football. It can be such a beautiful game but at the same time it can be the cruellest of games.
“You see the kids (crying) and I saw my own there, they’ve got tears in their eyes. They will take a bit of consoling, as will we all.
“But I am so proud of those boys for the achievement of getting to a major European final. They had no right to get to European final – a great achievement.
“It’s a massive disappointment but we have to to think of the bigger picture and what those boys achieved. Think of the nights they have given us – the nights against Dortmund, Red Star Belgrade, Leipzig – phenomenal nights.
“Of course it’s a disappointment but, I tell you what, they have got a cup final on Saturday.”
Rangers have thanked their fans following their Europa League final defeat.
The absolute heart break amongst the fans here...
How Sky Sports News covered the penalty shootout
A small group of Rangers fans gathered in George Square in Glasgow after the final whistle blew on the team’s nail-biting Uefa Europa League final with Frankfurt.
One fan said following the match: “They did us proud. We did really well and that’s what matters. You can’t ask for more than what they did.
“In life, you get defeated. If it wasn’t going to be this game it would be the next game.
“The atmosphere in Glasgow is really, really poor right now but I’ve had a good night.”
Another fan, Chris Strong, made his way into Glasgow from Stirling. He said: “Look at the supporters. It’s been buzzing. If you weren’t here, what would you be doing?
“It takes time. It took us 14 years.”
Statues in the area had been barricaded and memorial benches packed away in anticipation of crowds of fans making their way into the city centre.
Police regularly patrolled the area throughout the evening.