The Scottish Premiership leaders were knocked out of the competition by their rivals.
The Scottish Championship side booked their place in the final with a penalty shootout win after the game ended 2-2 after 120 minutes.
But despite the agonising defeat to Mark Warburton's men, Sviatchenko - who scored the Hoops' first equaliser at the start of the second-half with a fantastic header - has predicted that the squad will be able to put the defeat behind them in the near future.
"We will be behind everyone who needs it but they are all strong characters and they will bounce back," he told STV.
"Even though at this stage it is quite tough but we are all behind each other. From this stage we have to move on and show character and attitude."
The likes of Patrick Roberts and Tom Rogic may have the most challenging time putting the events at Hampden Park behind them.
Roberts missed a wonderful chance in the first-half when he had practically most of the goal to aim at with Gers stopper Wes Foderingham scrambling across following a previous dive in the other direction, while Rogic missed the decisive penalty in the shootout to send the Light Blues through.
Luckily for the Hoops, they boast an eight-point lead at the top of the Scottish Premiership so should have little problem seeing out the final five games of the campaign without too many stumbling blocks in the way of the side winning their fifth league title in a row.
So while they may not be able to fully banish the painful memories until they face the Light Blues next season, the fact that they should now go on to win the title should help the side get over Sunday's game.