The midfielder quit the Whites in the summer of 2019 and signed for SPL side Hibernian after spending seven years as a first team regular.
Vela had been with the academy from the age of nine and went on to make 182 senior appearances – more than any homegrown player since Kevin Nolan.
But his last 12 months at Wanderers were beset with rumours of disagreements with the manager – who had pushed Everton loanee Joe Williams ahead of him in the pecking order.
Now at Shrewsbury, the 26-year-old admits he knew the writing was on the wall.
"Our relationship went a bit weary," Vela told the Lion of Vienna Suite podcast. "It wasn't the best relationship at the end.
"We were playing Derby away and he wanted me to be on the bench, but I hadn't been on the bench for the previous three or four weeks.
"I said to him, 'instead of putting me on the bench, you might as well put a youngster on'. We had a bit of an argument and things went back and forward.
"We played Aston Villa the week after and he put me on the bench for some reason.
"I left and he didn't see me again after that."
After Parkinson arrived in the summer of 2016, Vela was placed front and centre in the Wanderers side looking to bounce back into the Championship and shared the club’s top-scorer award with Gary Madine on 10 goals.
"We had a good relationship at the start - for the first two years it was really good," Vela added.
"Then it just went a bit pear-shaped. I've got nothing against him, he was a good guy.
"But from my point of view, I loved the club and gave 100 per cent every game. But there were players on loan who were going back to their parent clubs - were they going to give as much effort as I would put into a game?
"That was my point of view but he never had it and just left me out.
"He's a stubborn guy who always thought he was right but I don't think that was the case."