Vettel was left incandescent after an attempt to pass Verstappen at Turn 1 led to the Red Bull driver running off track and maintaining his grip on third, the Dutchman then refusing to cede the position to the Ferrari over the remaining two laps, despite encouragement from his team to do so.
Vettel eventually inherited third after Verstappen was handed a five-second time penalty, but not before firing off several expletive-ridden messages.
"I saw the footage already," Verstappen said following the race. "Sebastian just starts shouting on the radio, using very bad language. I think he has to go back to school or something.
"I will speak to him, because he is a very frustrated guy at the moment. First of all shouting on the radio like a child, and then [gesturing] after the start finish - even more childish."
Verstappen also stood by his defence of what was third, saying it should have been treated in the same manner as Lewis Hamilton and Nico Rosberg's straight-lining of Turn 1.
"I think it's pretty similar to lap 1, corner 1 - Lewis [Hamilton] went off, gained a massive advantage," Verstappen said. "He went off, gained massive advantage - Nico too when we touched. I didn't even gain an advantage, I was the same length in front when I came back on. So yeah, I think it [the five second penalty] is ridiculous.
"If they don't give a penalty for Nico, don't give me one at the end..."