Chester claimed his departure was for `non football reasons`, but Wright countered that it was `totally football reasons`.
Wright said: "It was my decision. The position was untenable. I did not want it to happen, but it has.
"It's not the right time and I apologise for that. It's a very sad day. I know the side is a good side."
Assistant manager Dave Moss has also left the club, where Ray Mathias is now in caretaker charge.
Mathias has previous managerial experience at Wigan and Tranmere.