The race was temporarily stopped after 22 laps because of debris littered across the Baku city circuit.
In the fascinating aftermath of Sunday's race Hamilton had accused Vettel of acting in a "disgraceful" and "disrespectful" manner.
Vettel was penalised for deliberately driving into the Mercedes driver during a race restart in an act of revenge for Hamilton's supposed brake test on the German - which the FIA later cleared Hamilton of, having studied the data from his auto.
Hamilton and Vettel have won a combined seven F1 titles and more than 100 races. "Imagine all the young kids watching today, seeing that kind of behaviour from a four-time world champion".
Pressed on his collision with Hamilton, he added: "I passed him because he pitted, after the incident right there, side by side, I raised my hand".
"It happened, I don't think it was right but the biggest thing for me was that I lost the race through the headrest issue".
Sebastian Vettel, who extended his championship lead, steered his Ferrari into fourth, just ahead of Lewis Hamilton's Mercedes.
"I'm just looking forward to getting home". In the end we're racing as men.
"I controlled the pace, like all the other restarts I slowed down in the same spot", Hamilton said.More news: SpaceX launches 10 satellites from California air base
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"The stewards looked at my data and the reason I didn't get a penalty is because I clearly did not brake test him".
"The German's anger got the better of him and he reacted by driving alongside his title rival, gesturing with his left hand and veering into the side of Hamilton's vehicle". It's unsafe driving and to get a 10-second penalty for that.
"You saw what happen, I don't really care about it", said the Mercedes driver.
The flashpoint came as Hamilton bunched the pack up ahead of a safety vehicle restart which caught Vettel out and saw him run into the back of the Mercedes.
"I think Formula One is for grown-ups", Vettel concluded.
"I'm sure he didn't do it on goal but for sure it was not the right move. He's done something similar in China at the restart a couple of years ago so it's not the way to do it, I think".
"It's going to be a great championship battle throughout the rest of this year".
"Nobody wanted to see the schmoozing anyway, so now the gloves are off", said Wolff.
"They're warriors and you're at war at that moment, fighting for the race win and the championship", Wolff said.
"At a certain stage, the best ones that compete for the world championship in that phase of their careers can't be friends".