Giovanni van Bronckhorst's side fell to defeat in the most disappointing fashion in the Europa League final after Aaron Ramsey's miss proved costly in the penalty shootout.
While Frankfurt celebrated long into the night in Seville, they also proved themselves as gracious winners.
Although there were isolated incidents of violence, according to the Daily Record, Frankfurt fans were seen consoling Rangers supporters both inside and outside of the stadium with hugs, high fives and pats on the back after a largely good-natured encounter between the teams.
That feeling of goodwill has continued in the days since, with the German club sending a heartfelt message to Rangers supporters in the Daily Record, wishing them well for the Scottish Cup final against Hearts.
Across the back page of Saturday's edition of the newspaper, the statement read: "Rangers, it was an honour for us!
"You were a fantastic opponent with your countless fans. Together we showed how football should be!
"Emotional, passionate and fair. Greatness is revealed in defeat, especially in such dramatic fashion.
"Just like 62 years ago you are a great club. See you soon. Bring home the Cup this weekend. You earned it."
It was Ramsey's penalty miss that proved decisive on the night, and according to Jim White, the manner of Rangers' defeat was 'cruel'.
He told talkSPORT: "He will be in a world of his own, total dejection for him.
"There was so much responsibility at that moment, so much was riding on it, and he failed. That's the fact of the matter.
"He didn't come up to the spot and do what Rangers needed him to do and I'm afraid that's the moment that it swung in Eintracht Frankfurt's favour.
"It's a cruel, cruel process of events, we know that, and Rangers go home without this trophy."
But they have a chance to end their campaign on a high on Saturday as Rangers take on Hearts at Hampden Park, with kick-off at 3pm.