"Seriously? It is not the time for that," the 16-time doubles grand slam champion said.
Newcombe replied: "It's a joke".
Woodbridge said Maria was lucky to be treated courteously by the Australian wild child at the end of the match.
"Pascal Maria, lucky to get a handshake there I feel," he said.
"He could have influenced that match in a way that was totally unnecessary.
"He shouldn't get another match in the chair."
Newcombe praised Kyrgios for his maturity.
"Well played. He stuck in there. A very good, concentrated effort. He stuck to his guns."
Kyrgios' win sets up one of the blockbuster matches of the tournament when he takes on Scotland's Andy Murray in the fourth round.
Kyrgios and Murray have been scheduled to play in the final match on centre court on Tuesday morning (AEST).
Neither player was prepared to talk trash about the other following their third-round wins.
Instead, it sounded more like a bromance.
"It was love at first sight," Kyrgios joked of his relationship with Murray.
But now he is arguably the biggest obstacle standing between the 29-year-old Scot and the final of an event for which he is now the even-money favourite.
The pair have plenty in common, one aspect being that they defy simplistic labels.
Alert to a kindred spirit, Murray has frequently defended Kyrgios against charges that he is a charmless buffoon blessed with a magically loose right arm.
Another thing they share is a tendency to let off steam at their support box, and on Saturday Kyrgios went as far as calling them 'retarded' at one point of major frustration.
The world No 18 was suitably contrite about that, when asked if he had reflected on his choice of words.
"Yeah, definitely. I mean, it's all in the heat of battle," he said.
"I know some people can get offended by that. Im not meaning to be rude or disrespectful at all.
"Sometimes I'm just a pest. They (his box) are always doing the best they can do.
Everything I say and everything I do out there, they all know I love them. So, it's OK."
The end of yesterday's match saw another side of Kyrgios, the one who always tidies up his discarded water bottles and puts them in a bin to save others the trouble.
That does not come as a surprise to people who have dealt with him in his formative years on tour and will attest to the fact he has a natural smile as well as a snarl.
"He is good fun. He chats to everyone. I have never really seen him in a bad mood off the court," said Murray, who knows what it is like to be judged by what people see amid the stresses of his public workplace.
"Obviously on court, like I have many times, he has made mistakes, done stuff that is wrong.
"But when you see what some of the other players have done here - players who are better than him and won a lot more than him - the coverage they get for destroying a racket is much less than he does for saying to the umpire, "You have done a bad job" or, "You were terrible today". Because it is him, it is a bigger story."
Kyrgios has a very unusual, slightly old-school approach at odds with the punkish image he projects.
He does not have an official coach and sometimes does not bother practising. At Queen's Club three weeks ago, rivals looked on in astonishment as he went out to face Milos Raonic without any warm-up, just picking up his racket bag and walking straight from the players' lounge where he had been chatting, rather than prepare in the locker room.
What makes him dangerous, beyond any debate about his demeanour, is his prodigious natural ball-striking ability.
In his two previous Wimbledons, he has reached the fourth round and quarter-finals, including demolishing Rafael Nadal on Centre Court at this stage two years ago.
"Andy backs me up a lot. It's just good to have one of the best players in the world as a good friend like that," added Kyrgios in his paean to his opponent.
In the unlikely event of the underdog winning, Murray may have cause to regret his mentoring role, as the draw gapes wide open in the absence of Novak Djokovic.
"I think as soon as Novak loses, you look at Andy and you look at Federer's eyes lighting up,' reflected Kyrgios.
'They think that their chances have probably doubled. I think a lot of people in the locker room now believe they can win it. If the stars align and they're playing well, there are a lot of people who can go get it."
This is where an old hand like Ivan Lendl earns his money, drawing on experience to counsel Murray on handling expectations that could be overwhelming this week. There are already similarities with his title year of 2013.
"The year I won Wimbledon, I was seeded to meet Jo-Wilfried Tsonga in the quarter-finals and Roger Federer or Rafa Nadal in the semis, but they all went out early," said Murray in his BBC column.
"I remember that made it hard in terms of everyone focusing on me from early in the tournament and I spoke with Ivan about it at the time, because it's an extra thing to deal with." One advantage Murray has had in this rain-interrupted fortnight is his constant presence on Centre Court, and he could become the first player to go two weeks without facing a trial on Court One since Federer.
While not a massive factor, it is an advantage, although the Scot is keen to emphasise that he has not sought it out, but simply taken what the order of play committee have given him.
"Every year here I've always played one match on Court One and I asked to play the second round on Court One, so I have no issue going on there," he said.
"I don't make the decisions."
The chances are that Murray's superior movement and ability to mix speeds and angles will see him prevail, but Kyrgios beat him at the non-ranking Hopman.
