"I watched the fight on Sunday as a fan, but also as a coach, and I saw a lot of opportunities.
"I honestly believe from the bottom of my heart that not only would he have beaten Klitschko last Sunday, he would have knocked him out."
Barry was critical of Klitschko's dour approach to the Fury bout and said Parker's fast hand speed and footwork would be too much for the 39-year-old to cope with.
Whatever height advantage the 1.98m Klitschko might have over Parker (1.93m) would be levelled by the South Aucklander's quick punching ability and shot variation.
"You can't defend your heavyweight title throwing 16 power punches and landing a total of 56 punches in a 12 round fight," he said.
"Joe can land 56 punches in one round.
"The hand speed definitely cancels out a lot of the advantages that some of the taller guys may have."
Parker says Fury's victory will give heavyweight boxing a much needed boost and praised the Englishman for backing himself, both prior to the bout and in the ring against Klitschko.
"With Klitschko losing it brings a whole lot of excitement to the heavyweight division," said Parker. "The reason I say that is because if Klitschko had won everyone would say 'the champion did it again, he's won and was expected to win'.
"But it was an upset and Tyson, he talked a lot but he actually backed himself, and he did all he had to do to win.
"I thought he wasn't going to get the decision because it was in Germany, but I was happy he got the decision. He wasn't robbed, but he deserves it, he trains hard and worked hard."
