But the German’s Ferrari finished fourth behind race winner Max Verstappen, Valtteri Bottas and Kimi Raikkonen.
"That was a horrible way to do it to be honest," said Hamilton. "But I'd like to say a big thanks to everybody in this team."
Vettel and Hamilton collided at the first corner on the opening lap when the Ferrari hit the rear right wheel of the Mercedes. Both cars were damaged and returned to the pits, Hamilton with a puncture and Vettel needing a new front wing.
"I was trying not to be too aggressive there in the first turn and left a lot of space for the car behind," said Hamilton. "I kept coming back and I am proud to race for all the team. I have tried this year to work hard and do all I can in this team. I try not to leave any stone unturned in my preparation and that is the team philosophy.”
Vettel, who also four world titles, said: "I am disappointed, obviously. But it is not that important.
"It is more important to say well done to Lewis who has deserved the title and done such a superb job all year."
Vettel and Hamilton are joint third with the Frenchman Alain Prost on the all-time winners list. Only the Argentine Juan Manuel Fangio with five and Michael Schumacher with seven have been more successful.