Home favourite Whyte dropped his opponent twice but had to climb off the canvas himself in the 12th round, forcing him to hold on for the final bell to secure a unanimous points decision in a pulsating main event at the O2 in London on Saturday.
However, while all three judges were in agreement over the winner, scores of 113-112, 115-110 and 114-111 demonstrated the close nature of the bout.
Whyte was warned on more than one occasion during proceedings by referee Ian John Lewis but escaped any further penalties, much to Barry's frustration, as the deductions would have altered the outcome.
"I thought he should have had several points deducted," the Las Vegas-based trainer said in the post-fight news conference.
"I talked to the referee about if before the fight. I said, 'Look, we were not after any favours, we've had a rough time with officials, but let's make it a fair fight'.
"I said, 'We know this guy is going to punch after the bell, we know he's going to hit Joe to the back of the head, what are you going to do about this?'. He said, 'If he hits him in the back of the head, I will caution him and take points off him', and I said, 'Really?'.
"He cautioned him a couple of times, but of course he should have taken points off, one hundred per cent."
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Barry also pointed to the first knockdown as a crucial moment in the contest, with the New Zealander dropped in the second round after an apparent clash of heads.
Lewis, though, ruled a left hook prior to the contact had done the damage, leaving a dazed Parker to take a standing count.
"I think that was a round we were winning. It was a 10-9 round to us, to a 10-8 round to Dillian," Barry explained.
"When you talk about that headbutt, I think the effects from that were shown in rounds three and four, when Joe just wasn't himself. It wasn't until the fifth round that he had everything going again.
“But I'm really proud of Joe. I thought he fought a very courageous, gallant fight. We had a very short camp. It was a good camp, but a short camp.
"We knew that Dillian was a real physical guy. I expected him to bring out the best in Joe, make Joe fight, and that's the fight we all saw.
"I'm very proud of him, the way he dug deep in the later rounds and was an inch away from winning. It was a great fight for the fans, and it was a fight we needed. The Carlos Takam fight was a hard fight [in 2016], but this was a war."
Photo Getty Images. Caption: The referee intervenes in Dillian Whyte's fight with Joseph Parker