The Ibrox club were ejected from the first qualifying round of the Europa League by a team that finished fourth in their domestic league last season.
"It's an embarrassing result, given the investment (in the squad)," said Rae of his former club's 2-1 aggregate defeat.
"I have never seen them lose to a team of this calibre."
Rae, now 48, told BBC Scotland that he felt Pedro Caixinha's new-look team lacked the drive he would have expected to see as Rangers returned to European football for the first time in six years.
They had won the Ibrox leg 1-0 and in the starting XI in Luxembourg fielded four of their summer signings - Fabio Cardoso, Ryan Jack, Daniel Candeias and Alfredo Morelos, with a further two, Dalcio and Eduardo Herrera, making substitute appearances.
"They are only three or four weeks into their pre-season but with the quality that Rangers have allegedly brought in you would expect them to go through in a tie like this," said Rae, who played in the Champions League and Uefa Cup with Rangers in 2004 and 2005.
"It's OK if it's a one-off, you can lose cup games, but over two games you would expect them to get through.
"I was disappointed with the manner in which they played. They never got any combinations, there was no tempo or intensity and you could actually see it coming. It's as bad a performance and result as you're going to get.
"They just didn't create enough good chances. They had a couple of headers that you would have expected them to score, with (Niko) Kranjcar and (Josh) Windass and Kenny Miller hitting the bar.
"It would have to be up there with one of their worst performances and results in Europe. I think everybody is in shock.
"The way Scottish football is going, we're going to be a laughing stock."
Rae predicted that the Portuguese manager would come in for scrutiny in the coming weeks but he did not think Caixinha would resign or be sacked.
"He seems quite a confident guy in his ability and what he's trying to do," he said.
"The board have backed him to the hilt. I would expect them to back him and give him time to turn it around.
"The eight signings are just in the door. The season starts in four weeks. This will give Caixinha time to work with them. They will need to hit the ground running."
Alex Rae lamented Rangers' defeat by Luxembourg outfit Progres Niederkorn and fears it is likely to make Scottish football "a laughing stock".