Rae watched in horror as Rangers lost in Luxembourg to go down 2-1 on aggregate against Progres Niederkorn in the Europa League first qualifying round.
“It’s an embarrassing result, given the investment,” Rae told BBC Radio Scotland. “I have never seen them lose to a team of this calibre.
“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.”
Six of Caixinha’s eight summer signings featured in the Stade Josy Barthel. All but one of them, former Aberdeen captain Ryan Jack, are new to Scottish football and Rae warned them to expect a major reaction.
“I think they will all be shell-shocked,” he said. “It will be a rude awakening for a lot of them because for the next 24-48 hours the media will go to town on them because it is as bad a result and performance as you can get. So they will have to get their tin helmets on.”
The reaction came from further afield than Scotland with former England striker Gary Lineker incredulous.
The Match of the Day host wrote on Twitter: “Rangers lost to a club in Luxembourg. Not Luxembourg but a club in Luxembourg. Not the best team in Luxembourg, the 4th best in Luxembourg.”
Caixinha’s decision to ban his players from wearing green boots featured in several comments, including from former Celtic strikers Chris Sutton and John Hartson.
Sutton wrote: “Totally embarrassing from Rangers! Maybe concentrating on what goes on on the football pitch rather than boot colours would be wise...”
Hartson added: “Rangers out of Europe.. honestly it’s got nothing to do with wearing boots with green on them!!”
Former Liverpool midfielder Dietmar Hamann wrote: “Just seen Rangers result. Did their new gaffer ban green boots or boots altogether?”
The result made waves outside of football.
Writer, broadcaster and Millwall fan Danny Baker wrote: “Rangers beaten by 4th best Luxembourg team is real watershed. How could you hope for weaker opposition? Nolan Sisters? Cast of Love Island?”
Rangers now have a month without any scheduled games before they open their Ladbrokes Premiership campaign at Motherwell on August 5 and Rae believes Caixinha will be given time to make amends.
The former St Mirren boss, who was interviewed by Caixinha for a role in his backroom staff before Jonatan Johansson was appointed first-team coach, said: “He seems quite a confident guy in his ability and what he’s trying to do.
“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.”