Jimmy Campbell, 27, had just watched his team lift the trophy when he became pinned against a car park wall and dragged along the ground by the bus.
The father-of-one was left with a damaged spleen, bruised kidneys and widespread muscle damage to his torso after being caught unaware by the turning bus.
He is being treated in the high-dependency unit at Glasgow Victoria Hospital with recovery expected to take several months.
Speaking from his hospital bed, supermarket worker Mr Campbell, from Granton, told the Evening News he believed he was going to die and could only think about his fiancée and young daughter.
“What happened was that when we got to the pick-up point [after the match] I could not see our bus number,” he said.
“I spotted our rep at the gates as one of the other coaches was pulling up and I stupidly walked down the outside of the coach and the wall. As I did this the coach started to turn right, crushing me into the wall. Luckily I managed to roll myself a little when the bus hit me or else I would be dead.”
As he was struggling to breathe, a bystander rolled him into the recovery position with paramedics racing to the scene moments later. “I was awake the whole time but I thought that was me. I was lying there thinking I’ll never see my daughter or my fiancée ever again,” he said.
Doctors hope to release Mr Campbell, who is due to get married in September, later this week possibly into the care of Edinburgh Royal Infirmary before a long rehabilitation gets under way.
The Hearts fanatic said his accident “put a massive dampener” on an otherwise joyous cup final day out.
He said: “I wish I could have seen the team parade the cup on Sunday.
“To celebrate the win I had a small sing song to myself when the drugs kicked in but nothing much.”
He joked: “If it meant watching us lifting the big cup against the wee team I’d do it all again.”
A spokesman for Hearts FC said: “Everyone was shocked when we heard of Jimmy Campbell’s accident and we all wish him a speedy recovery.”
It is understood that no criminal action has been taken against the coach driver.
FIVE men were arrested during the Hearts victory parade, taking the total number held over cup final weekend to 35.
The offences on Sunday ranged from alleged assaults to breaches of the peace.
The men – aged 25, 17, 28, 27 and 17 – appeared at Edinburgh Sheriff Court yesterday.
A police spokesman said: “Of the tens of thousands who were involved in the match and celebrations, only a small number acted in an unacceptable manner.
“Both sets of supporters have been a credit to their respective clubs and we are grateful to them all.”