He lost his job at Loftus Road two weeks ago, and he suggested the social networking site Twitter was to blame.
That prompted the outspoken Barton to launch an attack on the 63-year-old yesterday, with him tweeting that Warnock was an "embarrassment" and comparing him to fictional manager Mike Bassett.
Neil Warnock: "I'm told Joey Barton had a few things to say about me on Twitter last night. Obviously, I'm disappointed with the comments, but I don't feel there's any need to respond.
"I don't have a problem with anybody at QPR and when I tuned in on Sunday to watch their match at Newcastle I was cheering them on.
"That might surprise people since I was sacked but most of the QPR players I brought to the club, many of them are the same players who did me so proud in winning the Championship last season, so obviously I want them to do well.
"I'm not bitter at all towards Tony Fernandes (QPR owner) and I was disappointed at the way some comments I made on TV this week were sensationalised by the tabloids.
"I was asked about tweeting and said it was a dangerous path to go down, when players and fans are tweeting the chairman, as one person's opinion could get undue weight, and it's hard to have much context in 140 characters.
"Then I picked up the papers and read I was "poisoned", which wasn't what I meant at all.
"I've had seven promotions and enjoyed every one but this one topped them all with what I've had to put up with off the field.
"The fans have been fantastic and I've had so many messages - even the owners, I'm so supportive of them. (Vice-chairman) Amit Bhatia, who took me to the club, will always be a special friend so I've got nothing but good to say about them.
"They've got a new manager now, Mark Hughes, who is a very good manager.
"I'm really desperate for them to stay up now for the hard work they have put in.
"Barton is a very, very good player and a very, very good trainer."