In a statement released via the League Managers' Association, Barton thanked Fleetwood chairman Andy Pilley, his coaching staff and the players as well as the fans for their "patience" but made no reference to the incident with Evans.
Barton said: "First of all I would like to thank the chairman Andy Pilley for the opportunity to manage Fleetwood Town. I have enjoyed every minute of my time at the club. I have learned so much over the past two and half years.
"There are some brilliant people at Fleetwood Town and I have enjoyed getting to know every one of them.
"I would also like to thank all of the coaching staff, both the ones I inherited and the ones I brought in. It has been some journey with some highs and lows and I have really enjoyed watching each of them get better every single day.
"I would like to thank the fans and say that I appreciate you sticking with me in my first management role. I am not naive enough to think I always got it right, but my only intention during my tenure was to drive this football club forward.
"I have nothing but good things to say about the people of Fleetwood and the surrounding community. I was welcomed from day one.
"To the players, thanks to each of you for bringing it every day. Nobody enjoyed playing against Fleetwood Town and ultimately that is down to you.
"Thanks for being patient with me on my coaching journey. I look forward to watching you as you continue to improve.
"It is tough times for everybody at the moment with all that is going on in the world. I am just a football manager who has lost his job, there are plenty of people who were much better than me at theirs that have lost them over the past 12 months.
"I will use this time out to keep getting better, until the next opportunity comes.
"All the best for 2021."