Warner has been condemned for the "despicable" incident after being banned from all cricket until the first Ashes Test against England begins at Trent Bridge on July 10 as well as being fined £7,000.
The condemnation of Warner, for punching Root in a Birmingham bar in the early hours of Sunday following Australia's 48-run defeat to England at Edgbaston in the Champions Trophy, has come from Cricket Australia chief executive officer James Sutherland.
Warner, recently fined by CA after becoming involved in a Twitter rant with journalists, has also been told that he needs to start making better decisions.
Sutherland also believes Warner, who at a media conference issued an apology for the incident with Root, will find it very hard to make the first Test team for the Ashes opener.
Sutherland told a press conference at the CA Centre of Excellence in Brisbane: "Warner's specific indiscretion is entirely inappropriate, there is no place for violence anywhere and I'm extremely disappointed in that, I'm extremely disappointed in him and I have told him that.
"In regard to David Warner himself I hope this is a turning point for him.
"I note that overnight he's made comments apologising for what he's done and expressing remorse for his actions.
"That's all well and good, it counts for a little bit but not much. What really counts is his actions going forward in the future and we're watching those very closely."
Sutherland believes Warner's chances of making the first Ashes Test are slim.
"Cricket people know it's going to be very hard for David Warner to be selected for the first Test. He can't play cricket until the first Test match starts.
"He's under no illusions to the direction his career is headed right at this moment. We have very high expectations that he will make much better decisions going forward.
"He's making some pretty ordinary decisions and getting himself into trouble and he's bringing the game and his team-mates and the team down. That's not going to be tolerated any much longer."
Sutherland confirmed five Australian players were in the Walkabout bar when the incident with Root took place ans has issued a warning to the whole Australia team, management as well as players.
"David Warner has done a despicable thing but I also hold the team to account here. There were other people there with him and those that were there need to take responsibility for that, but so does the team as a whole and the team management group as well."
Warner was joined by captain Michael Clarke when he issued his public apology.
In front of a packed conference room at a hotel in central London Warner said: "I struck Joe Root in the face, I'm here today to put my hand up and apologise publicly to Joe.
"I am responsible for my actions, extremely remorseful. I have let not just my team-mates down, but the Cricket Australia fans, the support staff, myself, my family, I'm sincerely apologetic."
The latest Warner incident has come at a bad time for the Australian team, just three weeks after he was also fined £4,000 for a Twitter tirade against journalists.
Clarke also had to take disciplinary action against four team-mates in March for failing to complete a team presentation.