Aaron Ramsey missed for Rangers in the shoot-out after coming on as a substitute with only three minutes left of extra-time, before Rafael Borre struck the winning shot to complete Frankfurt's remarkable triumph.
Borre was the hero of the night, after already cancelling out Joe Aribo's opener for Rangers as Frankfurt won their first European trophy since 1980 and booked their place in next season's Champions League.
"We are all heroes. Without the fans we wouldn't have made it," said Kevin Trapp.
Both clubs were looking to win a second European title in their history, Rangers after clinching the Cup Winners' Cup in 1972 and Frankfurt after they lifted the UEFA Cup 42 years ago.
But Rangers came up just short at the end of an incredible run to the final. Only ten years ago this week, Rangers fell into administration before being liquidated and relegated to Scotland's bottom tier.