"I was watching, I wanted to be in there," Parker said.
"It was really motivating watching that fight. And the support that we got was great recognition for our team."
Parker, friendly with both American Wilder, who retained his title after the draw, and Fury, predicted the fight would be close. In fact, he couldn't separate them beforehand.
Barry could, though. He predicted a knockout by Wilder and said Fury's display after two years of inactivity and huge weight gain and loss was "masterful". Barry felt Fury, knocked down in the ninth and 12th rounds but dominant in virtually every other, should have got the decision.
One judge awarded the fight to Wilder, one to Fury, and one couldn't separate them. In hindsight it's difficult to see how the judge favouring Wilder and the judge who scored it a draw could have given the American even six of the 12 rounds.
"He defeated huge odds - he showed a 6'9" man with tremendous boxing skills, light feet and fast hands is very, very hard to beat," Barry said.
"Wilder's reputation speaks for itself but he just couldn't time his punches, he couldn't time them with the power shot, and we all saw the frustration as he missed round after round after round trying to hit him with his big right hand.
"Fury's movement with upper body and lower body was tremendous. The way he was able to slip the right hand [of Wilder], it was beautiful boxing, no doubt about it.
"How anyone can do that to themselves 150lb of weight (68kg), the drug problems, the mental health problems and then come back ... even though he was on the canvas twice, he finished the fight the fresher man. Unbelievable. You have to give him huge props and you'd have to think if these guys fight a rematch that Fury would have to beat him easy the second time.
"I thought he was very unlucky not to get the decision."
Fury normally favours a swich-hitting style, but against Wilder he rarely took a southpaw stance. That's not to say he was completely orthodox, though, and his constant feints and movement of head and body made Wilder miss time and again. It was a display of skill which would cause Joshua, the IBF, WBA and WBO champion plenty of problems should the pair meet in the ring.
Far from making the division easier to follow, the draw has made it more complicated. Joshua was expecting to fight Wilder at Wembley in April but Wilder and Fury may instead fight again.
"The division from here - there's a couple of ways of looking at this," Barry said. "Does Wilder want to fight Fury again because it's his choice. Was Dillian Whyte the biggest winner last night? Does this mean he will fight Joshua? I would say there is a pretty good chance that these guys [Wilder and Fury] will fight again in April or May next year.
"The only concerning thing for me is... Deontay Wilder has now defended his title eight times, he was fighting in the US and he was the underdog - the crowd was a British crowd."
A re-match would almost inevitably be in the United Kingdom because of the support for boxing there and Fury's reputation – which he enhanced significantly with a courageous and skilful performance which would have won him a lot of new fans.
Patrick McKendry travelled to Los Angeles with assistance from Flooring Xtra, a major sponsor of the Joseph Parker v Alexander Flores fight at Christchurch's Horncastle Arena on December 15.
