McKay reunited with former boss Mark Warburton at the City Ground this summer for a £500,000 fee after the winger was dropped from the first-team squad.
Grant Smith, McKay’s agent, insists Rangers could have secured double that amount had Caixinha played his hand better during negotiations.
He told the Fitba Hacks podcast: “Barrie was their main asset because the rest were older. OK, you might have got your money back on some of them but Barrie was someone who was going to make them real money.
“Forest were interested and they made £15m on a player. Then Pedro decided not to involve him. Yeah, he ostracised him.
“If I’m in charge of Rangers at that time, I’m asking ‘What are you doing?’ But what’s Rangers’ leverage?
“They told them they didn’t want Barrie. If you tell a buyer you want this player to stay – that’s your leverage. Soon as you put him with the youth team then you don’t have any leverage.
“Forest would have paid a lot more. Easily. Double at least. Mark knew him, Davie Weir knew him and they knew the situation. Rangers took their poker hand away from themselves.
“I mean, some of the stuff Pedro said to him. He was contradicting himself all the time. One minute saying he was the best player in Scotland, the next he was putting him with the youths.
“Someone doing the job of that size should have been doing better. He cost Rangers a lot of money.”