The Celtic winger, on loan from Manchester City, was presented with a golden opportunity to level the scores after Kenny Miller’s 16th-minute opener.
Shortly after the half-hour mark Leigh Griffiths’ shot bashed back off the post and Roberts was left with the seemingly simple task of converting the rebound past goalkeeper Wes Foderingham, who was still picking himself off the ground. But the 19-year-old prodded his effort into the side-netting.
While Celtic equalised early in the second half and clawed their way back into the game again in extra-time before losing 5-4 on penalties, there was no preventing Roberts from blaming himself.
“I felt like I’d let myself down, personally,” he said. “Any other day, I would put that away. It just wasn’t meant to be today, obviously. I’m just devastated, we all are.”
He believed it would have been a different story had he managed to bring Celtic back into the game in the first half. “With the chance, I should have scored it,” he said. “There are no excuses for that.
“Did I have too much time? No, I should be scoring. Looking at the game overall, we weren’t good enough – and that’s why we lost.
“The atmosphere was exactly what I’d expected, I knew what it would be like. But, right now, it just feels rubbish.
“In the dressing room just now, we were all absolutely distraught,” he added. “To go out on penalties is the worst way we could exit this competition. Having said that, we just were not good today.
“Did we deserve to lose? On chances, we obviously had mine – and Griff [Leigh Griffiths] hit the bar. We scored twice to get back into the game. But we weren’t at our best today. Far from it.”
Roberts was not the one in the sights of the majority of Celtic fans, who turned their ire on manager Ronny Deila at half-time, and again at the end of the first half of extra-time, with Celtic trailing 2-1 after Barrie McKay’s stunning strike.
But Kieran Tierney, the teenage left-back, backed Deila, and, like Roberts, stressed the players were to blame for the loss.
“All of the players are behind the manager, 100 per cent all the way,” he said. “The players didn’t perform in the game. He has shown faith in all of us in that team and we back him.
“I can understand the anger of the Celtic fans because I am one myself. Obviously, we went out there and didn’t perform to our best, so we are all devastated.”
Charlie Mulgrew, meanwhile, was similarly dejected. He is not even certain if a league title win can make up for such a depressing defeat to their fiercest rivals, particularly given Rangers’ current lower league status.
Celtic, eight points ahead of Aberdeen at the top of the Premiership with five games left, are back in league action on Sunday against Ross County.
“We’ve lost an Old Firm game and nothing really makes up for that,” said Mulgrew. “It’s done though, and we need to concentrate on the next thing now which is winning games for Celtic and winning the league.
“This game will need to be put behind us, and as hard as it will be, we have to move on.
“We’ve got to try and win everything in this country, and that was our aim today, to get to the final of the Scottish Cup. It’s always a great day at the end of the season, but we’ve not got that now. We’re gutted.”