McAvoy was sacked on Monday evening after just six months as permanent head coach, having done the job on an interim basis since March.
On Wednesday afternoon, the Scot issued a statement through the League Manager's Association.
In the statement, McAvoy said: “For the past four-and-a-half years, I’ve had a fantastic time at Preston North End FC which unfortunately, has now come to an end.
“Being offered the role as head coach at the end of last season, after the team did so well in the final eight games of the Championship, was an honour and a privilege for my family and myself, and an opportunity I could not turn down.
“I am truly grateful to the late Mr Trevor Hemmings, Peter Ridsdale and the Hemmings family for giving me the opportunity at this wonderful football club.
“I leave the club with great memories, from both of my roles as first-team coach to Alex Neil and recently, as head coach.
“I have loved working with the backroom team and the players on a daily basis and I would like to thank them for their effort, commitment and support during my tenure as Head Coach, it is greatly appreciated.
"My thanks also go to the fans, who always supported the team and me during the 33 games I was in charge.
“I wish the team all the best against Barnsley on Saturday and beyond and I am confident that they will be successful under my successor Ryan Lowe, as the team spirit in the dressing room is fantastic.
“Finally I would like to thank every member of staff at Deepdale, our training ground at Euxton, and our academy at Springfields, as well as all the young, full-time academy players I had the privilege of working with.
"Goodbye and best wishes PNE."
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