The Hoops' interim boss Neil Lennon slated his men after the Irn Bru First Division side dramatically and deservedly won through to their first final since their formation in 1929.
Steven Craig and Martin Scott scored the second-half goals which sparked wild celebrations in Dingwall and had Lennon promising a clear-out at the end of the season whether or not he is still at the club.
The Celtic defender, 19, insists the players will have pacify the disgruntled fans when the Steelmen travel to the east end of Glasgow in the Clydesdale Bank Premier League.
"The defeat was horrible," Thompson said.
"The fans deserved more and we let the manager down.
"Everyone knows it wasn't good enough, it's not what Celtic are about.
"I can't put my finger on it, it seemed they were winning the second balls and we didn't play as well as we can.
"The next game is on Tuesday against Motherwell and we have to go out and show pride.
"We have to redeem ourselves to the fans.
"That's the motivation now."
As the Parkhead club lick their wounds after a defeat which rivals previous cup shocks against Clyde, Inverness and Raith Rovers, Lennon's bid to keep the job is in tatters.
The Irishman kept his players in the dressing room for 15 minutes after the game and strikers Georgios Samaras and Marc-Antoine Fortune, in particular, came in for some stinging criticism.
However, the big Greek striker, who hit the post when Celtic were trailing 1-0, kept his counsel.
Asked if Lennon was still the man for the job, Samaras retorted: "Yes, 100%."
Then asked to expand on what was said in the dressing room by Lennon, the former Manchester City striker replied: "What happened in the dressing room stays in the dressing room.
"Our biggest target this season was to win the cup and it didn't work out.
"The only thing we can do is keep our heads up and we have another difficult game on Tuesday.
"We have to prepare for that.
"It is difficult but we must play for our pride."