Dennis had accused the world champions of inciting Dan Fallows to break a legally-binding contract he had signed with McLaren and indicated the dispute was likely to go all the way to the High Court.
"We're obviously not too happy to be contracting people in a correct and professional way only to find that those contracts are disregarded," Dennis told Britain's Sky television before Sunday's Chinese Grand Prix.
"People don't just change their mind. They are induced to change their mind. And people being induced to breach contracts, it's just wrong...you can either just ignore it or you can do something about it."
Red Bull team boss Christian Horner said he had "the utmost respect" for Dennis but was not sure what the Briton was talking about.
"You can't force someone to work somewhere they don't want to be," he said.
"He (Fallows) signed a contract with McLaren with people that aren't there any more and decided he didn't want to go. That's the way it is. It's not something that Ron's unused to. It's something that's happened to him quite often in the past."
The legal tussle between two of Formula One's biggest teams has resulted from a major recruiting drive by McLaren, who have not won a race since 2012 and failed to appear on the podium at all last season.
Dennis has ousted former principal Martin Whitmarsh at the helm of the team, bringing in Eric Boullier from Lotus as racing director, since Fallows was contracted.
Fallows, who was put on 'gardening leave' by Red Bull last year, had been due to join McLaren before the start of the season.
However, Red Bull announced this month that the Briton was returning to them as head of aerodynamics to take over from Peter Prodromou, Adrian Newey's right-hand man, who is moving to McLaren.
"He (Fallows) left for his own reasons but then the situation changed with Peter going and he approached us and said 'The situation is different at McLaren now, can I come back'," said Horner.
Asked whether it hurt to have his ethics questioned, he smiled: "Not when it's from Ron Dennis."
Newey, Formula One's top designer who has won championships with three different teams, joined Red Bull from McLaren in 2006 despite Dennis's best efforts to keep him.
Dennis, who ran McLaren from 1982-2009 before focusing on the company's growing sportscar business, denied that Fallows' contract had been signed by Whitmarsh.
"In fact, it wasn't signed with Martin at all," he said. "It was one of our managers.
"We've recruited huge quantities of people over the last few months and some have joined the team quickly and some are on 'gardening leave'...we try to do things very professionally and correctly."
The McLaren boss, whose team are currently third in the championship with Red Bull fourth, called on Horner to 'reach out' and discuss the situation, but said emails had been ignored by Red Bull.
"The onus is on Christian stepping up to the plate and sitting down and talking," he added. "My door's open...he knows my mobile number, he can call me any time."