Gianpiero Lambiase (GP), who has worked with Verstappen for some eight years and is known for standing up to the driver in forthright fashion, had a series of exchanges with an increasingly unhappy Dutchman at the Hungaroring.
Verstappen had complained about Mercedes' seven-time world champion Lewis Hamilton's driving after they collided, with the Red Bull pitched on its nose and off the track in a battle for third.
"I am not even going to get into a radio fight with the other teams, Max," Lambiase said.
"We’ll let the stewards do their thing. It’s childish on the radio, childish."
The comment raised eyebrows for its tone, between individuals with one of the closest driver-engineer relationships.
Horner said Lambiase was not actually referring to Verstappen, however, but the radio traffic from members of rival teams seeking to push the stewards into penalising him.
"I don't think GP's reference at that point was in reference to Max," he told reporters. "Others (were) obviously goading for penalties because obviously the stewards are listening to the radio as well."
Verstappen, who finished fifth after seeing stewards who took no further action, was not backing down afterwards when questioned about his radio messages and the swear words bleeped out for the global television audience.
"I don't think we need to apologise," he said. "I just think we need to do a better job."
Horner said the team would discuss behind closed doors what they should have done better.
He added that Mexican Sergio Perez had done a good race, one of his best in months, in going from 16th on the grid to seventh.
"He had good pace and made some good passes and hopefully will have taken a lot of confidence out of that," Horner said of a driver whose future remains uncertain, despite recently signing a contract extension.
Perez has scored only 21 points from the last seven races, compared to Verstappen's 129 in the same period, and is now seventh in the standings.
The Mexican is also the only one of the top eight without a win this season.
