As Christian Horner and Helmut Marko hit out at Lewis Hamilton in the aftermath of the British Grand Prix, the bad feeling spilled over into social media, with the British driver suffering abuse.
"The comments that were made, surely out of emotion, were going directly against a seven-time world champion," he told Sky Sports.
"Words like 'amateurish' should have no place," he continued, "and what it triggered was an avalanche of comments in the social media, a lot of controversy, added to further polarisation and I think we as a sport should do the contrary. We should de-escalate."
The Austrian was also keen to react to continued claims, including by Verstappen himself, that Hamilton and Mercedes were "disrespectful" in celebrating their win whilst the Dutchman was hospitalised.
"You can only rely on the information that you have," he said, "and the information we had at the time was, from Christian himself, that he was unharmed.
"From another senior member of the Red Bull team that I asked, he was okay and was doing fine," he added. "We also asked the media on the way to the podium whether he was okay and everybody said he’s fine.
"So we won the British Grand Prix after losing five races... it was Lewis’ home grand prix and that’s why the celebration was high.
"But again, it depends from the perspective you’re looking at. If the Verstappens are in hospital for precautionary checks and he didn’t feel well, then you’re seeing that in TV while you lost, also as a competitor you can have that perception and that needs to be respected."