St John, 79, said Liverpool should have won the cup in 1965 – two years before Jock Stein and the Lisbon Lions won the trophy for Celtic.
Shankly’s side led Inter Milan 3-1 from the semi final first leg, but went out under controversial circumstances following the return, where Milan were awarded two disputed goals.
Former striker St John – who also had a goal ruled out by the late Spanish referee Jose Maria Ortiz de Mendibil – claims Liverpool missed out on a place in the final because the referee “was got at”.
Speaking on documentary “Shankly: Nature’s Fire”, broadcast on BBC Two last night, St John said: “Had we beaten Milan over there and got through we could have won the European Cup.
“Shanks would have been the first manager to do that. It would have been great for him and I think about that.
“I think ‘did we let you down boss’ but that was out of our hands, the Milan game in Milan, when we were cheated out of it.
“Shanks was told, you’ll not win this game with this referee, and it was a fact. Without a doubt, he had been got at.
“But the boss went on and we were still picking up trophies.”
Shankly led the club to unprecedented success in the 1960s, with a side featuring several Scots including St John, Ron Yeats and goalkeeper Tommy Lawrence.
The European Cup was the only major award that eluded the Scot, although he laid the foundations for his successor Bob Paisley to lift the trophy three times in the 1970s.
St John told the documentary of his grief after Shankly died in 1981, and how the statue that stands outside the club’s Anfield stadium could not be any more apt.
He said: “He was a unique man. The statue is so apt; the inscription on it ‘he made the people happy’. You couldn’t have thought up a better line for him.”
Shankly, who grew up in the Ayrshire mining village of Glenbuck, remains one of the most iconic managers from a golden era of football.
Kevin Keegan, 66, who also starred for Liverpool under Shankly, said the Scot would not have enjoyed football as it is today.
He said: “It’s not his idea of football, and I think he would be looking down and thinking ‘it’s changed and I’m not sure it’s for the better’.
“He wouldn’t like the players putting on earphones and walking off the bus without acknowledging the fans and signing a few autographs. He’d hate that.
“He probably wouldn’t even like the advertising on the front (of the shirts) – I think he just liked the badge.”