Wednesday's trouble first flared in Piccadilly Gardens after a technical fault with a big screen left up to 20,000 fans frustrated.
Riot police were sent in as violent clashes broke out along nearby Market Street, Oldham Street and Newton Street.
Pc Regan, from Offerton, Stockport, was on duty for public order and not riot control, but said he sensed the mood was darkening as he listened to the police radio on the way in to the city.
"From the outset we were bombarded with bottles and cans as we tried to contain and disperse the crowd," he said.
"It was unbelievable when we got there - it was already in motion. It was frightening, on a different scale from any other match I have worked in my 23-year career."
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Pc Mick Regan describes how one Rangers fan tried to help him
As the trouble wore on Pc Regan and a handful of colleagues found themselves being pushed down Newton Street by a mass of fans hurling bottles.
The officer said he got into trouble after being hit by a bottle from a distance of about 4ft which struck his elbow, then he found himself on the ground.
Pc Regan told BBC News: "The next thing I knew I was getting kicked in the body, on the legs.
I'd have been seriously injured... I knew I was going to get done over
Pc Regan
Asked if his attackers could have killed him, he replied: "I try not to think about that... I wouldn't say they were trying to kill me but I knew if they got me they'd have seriously injured me."
Pc Regan escaped with sore ribs and a puncture wound to his arm.
He said if it had not been for someone who pulled him away from the melee he would have been more seriously injured.
'Alcohol the problem'
"I saw two lads coming from my right; I thought they were going to have a go," he said.
"But one of them shouted at me saying, 'I'm British Army, I'm a medic'. He grabbed me by the collar and he propelled me up the street.
"If they had not come along at that point I'd have been in big trouble. I'd have been seriously injured. I knew I was going to get done over.
"I feel lucky; whoever that Army lad was, he wants a medal."
But despite the widespread condemnation of the Rangers fans, Pc Regan said many of the supporters he came across were "as good as gold".
Pc Regan told the BBC he felt alcohol was the cause of the biggest problems, especially among the hardcore who caused the trouble.
"Those particular people were just out to cause harm to any police officer. It could have been me - it could have been anybody," he added.
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