Barton attacks Warnock on Twitter
Warnock, who signed Barton from Newcastle in August and immediately made him his skipper, lost his job with Rangers earlier this month with the club hierarchy concerned that he was presiding over an immediate return to the Championship.
The 63-year-old expressed his disappointment at the decision on Thursday, telling the BBC that he thought owner Tony Fernandes had been "slowly poisoned" against him.
Warnock added that he thought some of the damage had been done via Twitter, saying: "It would have been difficult to resist because people get on the phone and tweet and it's almost like slowly poisoning somebody from outside the club and, no doubt, from within the club as well.
"It's a dangerous precedent. If you let players talk to the chairman but, you know, you can't stop tweeting."
Warnock did not specifically name Barton, but the midfielder, a prolific 'Tweeter' who was sent off in Warnock's final Premier League game against Norwich, took to the social networking site on Friday afternoon to respond.
He wrote: "Neil Warnock saying I talk to much. Now that is funny. Lost his job and the guy is blaming everyone but himself! Embarrassing, time to look in the mirror mate. Last thing we need right. Big week."
Then, in a thinly-veiled assessment of Warnock's managerial capabilities, he added: "If I talked about Neil, he'd do well to get another job. Twitter cost him his job???? I can think of a million other things! #shutitwarnock.
"Looking forward to the game against Wigan tomo. 1st time in a while we actually have a plan and seem organised. #3ptsneeded."
Barton, who also compared Warnock to fictional manager Mike Bassett, is no stranger to controversy on Twitter, having previously attacked the board of former club Newcastle on it.
He has also made a number of radical suggestions, such as claiming clubs should be able to sue referees after he was sent off following an altercation with Norwich's Bradley Johnson.
When asked about his player using Twitter on Thursday, before his war of words with Warnock, Barton's new manager Mark Hughes said: "The only issue most managers have with Twitter and Facebook is whether issues or details that should be kept in-house are broadcast to a wider public.
"That is my only concern from a personal point of view and I don't think he has been guilty of that in the past and I don't anticipate he will do in the future.
"That would be my only concern from a personal point of view. It is part of his life, he enjoys that. Some guys like a game of golf, some play snooker, Joey seems to Twitter all day. I haven't got a problem with that."