Former Hibernian and West Brom manager Mowbray rejected those claims in the strongest possible terms on Wednesday, while the Parkhead club announced they were taking legal advice over the issue.
Speaking on Celtic's online channel, Channel 67, on Thursday Mowbray hit out at the press.
He said: "The story of Scottish football really isn't big enough for the newspapers that are out there and they try to create an agenda that can run for a few days and can cause a bit of unrest.
"It gets reaction from supporters, it gets letters pages going, it gets the back page the following day because there's reaction.
"It doesn't affect me but I know it affects our supporters.
"Why do I speak to the press? Really to talk to our fans - that's the only reason that I talk to the media.
"If it was down to me solely, I would probably end up doing all our media stuff to our supporters through mediums like yourself (Channel 67) and Celtic View (the club's official magazine).
"Maybe there's a proportion of our fans who don't have access to Channel 67 or have the opportunity to buy the View, and their only knowledge of Celtic Football Club is through the daily newspapers.
"That's, in my mind, why I give the courtesy to talk to the newspapers."
Mowbray insisted he did not have a problem with the media in general, but claimed there were "few agendas" against the club.
He added: "I've spoken to the last two Celtic managers, who tell me, 'don't get over-concerned about it because it's never personal - every Celtic manager gets that'.
"I do get to hear these stories - the Scott Brown story this week, which did need addressing of course because it was a total untruth and had no substance to that whatsoever.
"People just can't make stories up and write them: it should be allowed to happen, which is why the club are taking action, I think."
Mowbray believes he was afforded "a lot more respect" during his two-and-a-half years in charge of Hibs.
He said: "You're trying to compete with the Old Firm, trying to build a young team, trying to play entertaining football, and that was seen as a positive.
"Whereas most things you do over here are generally tried to be spun to make a negative story."
Meanwhile, Mowbray believes Landry NGuemo's involvement in the African Nations Cup has had as big an effect in the last two games as the club's injury problems.
Midfielder NGuemo is currently in Angola with the Cameroon squad and sat out Saturday's Clydesdale Bank Premier League game with Falkirk and Tuesday night's Active Nation Scottish Cup tie at Morton.
Mowbray said: "We are fully stretched at the moment.
"There are injuries to some very, very key players.
"I think the loss of Landry to the African Nations Cup - particularly while Scott Brown is injured - unbalances the side a little bit regarding winning the ball back.
"The squad has coped okay. We got through to the next round of the cup in what was a tight, tight game away at Morton.
"Last weekend against Falkirk, obviously we're disappointed only drawing that game.
"But I thought there were a lot of positives, some debuts, some young players showed the potential that they have for the future.
"I don't think it'll be long before the likes of Scott Brown, Shaun Maloney, Scott McDonald will be back out there competing, back in the team and hopefully driving us on to victories."
Mowbray revealed he still hoped to make "one or two" more signings before the transfer window closes.
"The work continues on a daily basis, lots of calls and working until pretty late in the evening to try to progress things along," he said.
"I'm pretty hopeful that would be the case, that there will be one or two more new faces in the door before the end of the month."