Hamilton got off to a disastrous start when he collided with Sebastian Vettel on the first lap.
The four-time world champion questioned the Ferrari driver’s intentions as he was forced to pit but eventually drove his way to a ninth-place finish while Vettel came in fourth.
Allison admitted it was not the race they wanted but nevertheless was overjoyed with the result in the end.
“This was definitely an ugly race. We left the last race buoyed up by having got the Constructors’ Championship but we know that probably means more to us than the world,” said the Mercedes chief.
“This is the one that counts and I think after a season we’ve just had, it’s hard to imagine a champion who deserves it more than Lewis does.
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“He’s just driven his socks off all year long. Lewis is right at the apex of his career and one of the all-time greats in this sport.
“To be alongside him while he gets his fourth championship in an extraordinary season of ebbs and flows and high drama is just brilliant for all of us.”
“There’s no doubt Ferrari and Red Bull are fierce competitors. It’s going to be a very difficult season next year.
“This is the most exciting and difficult year in many, many years and Lewis has driven it to perfection. It would be very hard to put him anywhere other than at the top because he is a class act.”
Meanwhile, Max Verstappen cruised to victory in Mexico after a brilliant manoeuvre on the first corner set the Dutchman on his way to a third race win of his F1 career.