The 22-year-old was sold to Nottingham Forest earlier this month for a fee believed to be around £500,000 after rejecting a new contract.
Prior to his departure, McKay was omitted from the Rangers side for both of the club’s Europa League matches with Progres Niederkorn.
This came after his role in the team was reduced the previous campaign following the arrival of Pedro Caixinha, who replaced Mark Warburton at Ibrox.
When Warburton came back to sign the player for Forest, McKay jumped at the chance to reunite with the man who helped kick-start his career in Scotland.
The player told BBC Radio Nottingham: “There was a change of manager and his opinion was different.
“I wasn’t being treated the way any human being should be treated, but that’s football and I had to move on.
“It made the decision easy for when the gaffer got on the phone and he was obviously a big factor in me coming here and working with him again.
“When he came into Rangers, it was a big stage of my development and he helped me improve as a player.
“The way things happened up there is more disappointing. I spoke to my family, spoke to my girlfriend, spoke to my agent and I think it was just the right time.
“I guess that’s football, but I’m a big boy and will get on with it.”