The Luxembourgers sealed a 2-0 home win on Tuesday to go through 2-1 on aggregate, marking their first victory in a UEFA tie in 14 attempts.
A delighted Amodio told BBC Scotland: "It's a great event, amazing.
"I cannot believe that we won 2-0 against Rangers. It's not possible. We made history and I can't believe it. It's incredible."
Ahead of the match, Gers boss Pedro Caixinha had described the possibility of defeat as "unthinkable", but his side – who did hit the crossbar twice in the closing stages – produced a limp display.
The Portuguese shouldered the blame and was apologetic to the club's supporters after one of the worst results in Rangers' history.
"We need to apologise to our fans because they gave us support and loyalty, they don't deserve this," he told Rangers TV. "I assume all the responsibility.
"We could not do what we were here to do – win the game. It's something that happens once in a lifetime – it happens to us today."