Catterall - the WBO mandatory challenger - produced the performance of his life against Taylor, the undisputed junior welterweight champion, but was on the wrong end of a split-decision verdict.
Taylor got dropped during the fight while both fighters were each docked a point for offences.
Doncaster judge Howard Foster scored it 113-112 in favour of Catterall but Victor Loughlin gave the fight to Taylor by the same scoreline alongside a score of 114-111 by Ian John-Lewis.
Davison - who has worked with Taylor in his three most recent fights, including a unification win over Jose Ramirez in Las Vegas - says the reaction in the UK was not the same compared to the US.
"If it was that controversial in America, they would be saying the same thing," Davison said.
Replying to Simon Jordan on talkSPORT after being questioned on what he said, the trainer added: "Because what I am saying is, these people who have all these opinions - put out your scorecard and if they've all got the same exact rounds - 'Jack Catterall won this round, Jack Catterall won that round, Josh Taylor won that round' and if it all matches up - but it wouldn't.
"The rounds were hard to score. I can guarantee if we picked 20 random people to score that fight sat on their own, I guarantee you the rounds that they gave Jack and the rounds that they gave Josh would be different.
"What does that tell you? That the fight was hard to score. A fight isn't scored overall, a fight is scored round by round," Davison added in reply to Spencer Oliver.
"If people are giving Jack and Josh different rounds, what does that tell you? It tells you that there is an argument for Josh winning that round when someone else thought Jack won the round."
Joshua needs to control the ring
The pair are likely to meet at the end of June but Joshua will be without Rob McCracken after departing from the Team GB trainer following his points loss to Usyk in September.
"If you can't control the ring, how are you gonna control the opponent?" Davison explained.
"He was so fixated on the fairy-tale, textbook, foot on the outside, southpaw-orthodox. Well look at what happened when Usyk knocked out Tony Bellew - his foot was on the inside.
"He [Joshua] was so focussed on trying to get his foot on the outside, he constantly allowed Usyk back to the centre of the ring.
"Anthony Joshua's not gonna win the battle in the middle of the ring, clearly. So he has to be able to control the ring, he has to be able to make Usyk work harder than Usyk wants to work.
"If he can control the ring and create scenarios - because that's what wins fights, scenarios that favour Anthony Joshua - then he has a chance.
"But to be able to do that he has to control the areas of the ring and where the fighting takes place."
"He has to be able to control the ring, he has to make Usyk work at a faster pace than what he wants to," Davison said when asked if Joshua has a chance of overcoming Usyk.
"Don't get me wrong, southpaw-orthodox - there's always gonna be an element of lead hand and a bit of lead hand play to the battle of southpaw-orthodox.
"But to be stood in the middle of the ring and allow Usyk to dictate, he's never gonna dictate and win that lead hand battle at that tempo, it's never gonna happen.
"He'll get out-thought and therefore out-fought.
"If Joshua can control the areas of the ring, push Usyk back, make him skirt around, make him break his base, attack when he breaks his base, then he's gonna have a lot easier entries, a lot safer entries and he'll land cleaner, more often.
“I think with the right tactics, Joshua has the capabilities to win the fight. With the right game plan, the right preparation.
“Is he capable of winning? Yes. Do I think he’s going to win? Probably not. But I’d love to see him win because I’d love to see that fight [with Tyson Fury].”