In his first year in charge, Barton has turned Derry’s season around after a heavy defeat by Tyrone two months ago and believes the only way to answer his critics might be to quit while he’s ahead.
The Oak Leaf manager was angered to read last week that he and Cavan boss Terry Hyland had had “a stay of execution” because they’d won second round qualifiers the previous weekend.
“I think it’s a disgusting disgrace,” said Barton.
“You are looking at a manager (Hyland) who brought a team up to Division 1 this year, arguably a very successful year, while I am in my first season and people are talking.
“What a load of nonsense.
“I am fed up of these people talking nonsense. I am not interested in speaking to them.
“They know nothing about football. What they want to do is stand on the sideline and come and get involved with a team where it’s 24/7. I have nothing to prove.
“You know this, if we get over Round 4, I might just quit. Quit whenever you’re ahead!
“That would seem to be the sensible thing to do rather than people talking nonsense next year.”
After qualifier wins over Louth, Meath and Cavan, Barton’s team play beaten Munster finalists Tipperary on Saturday for a place in the All-Ireland quarter-finals.
Reaching the last eight would be a resounding success story for Derry, considering they were hammered 3-14 to 0-12 by Tyrone in the Ulster championship at the end of May.
“Derry have fantastic footballers,” Barton claimed.
“I think the mental pressure of the Tyrone game... we heaped a lot of expectation upon ourselves. Once that went, the boys had time to recover.
“But sure, we weren’t meant to get this far!”
Barton also praised his captain Mark Lynch, who scored 0-6 against Cavan at Kingspan Breffni Park last Saturday and has been hugely influential in recent victories.
“There is justice, because there is nobody more committed than Mark. His application and commitment to Derry I would never have known until this year. I am not patronising him in any way.
“What an inspirational leader he is. He is a fantastic player and it’s about time he started playing a bit.”
Another Derry forward, Emmett McGuckin, insists his side can live with the favourites’ tag against Tipp.
The 25-year-old Magherafelt clubman hit 1-1 against Cavan and thinks his team have the impetus to drive on and reach their first All-Ireland quarter-final since Dublin beat them 0-18 to 0-15 in 2007.
“Any game at any stage of the year gives you momentum, it gives you that bit of belief. Within our squad, within Derry, everyone knows the ability is there. But you have got to go out on the day and prove it.
“You have got to just take it game by game. When you win it’s a great feeling and it does give that sense of togetherness in the squad. The back door is a great way to get back into the competition and you can only go and do your best.
“Again for the third game on the trot we go a bit of momentum from a win. But you can’t take anything for granted yet, you have got to just go to the next game and drive on again,” he said.
Derry have not won an Ulster title in 18 years but McGuckin believes the talent is there in the county.
“Ulster is a difficult one, it was a big game against Tyrone and everyone knows we just didn’t show up that day. But within ourselves we know we have the potential and the ability in Derry.
“It is days like the win over Cavan when the crowd starts to get behind us and everybody is starting to believe again. You come up and you see Derry club football, it’s ding dong every game.
“To put it together and finally get a result like that, it’s really impressive, and it’s a massive achievement for us. But it’s only a step in the line and we have got to keep going.”