Hamilton was on course to win a record-breaking eighth world title having dominated the 2021 showdown until an incorrectly-handled Safety Car period turned the race - and the outcome of the championship - on its head.
The Mercedes driver was overtaken on the final lap by Red Bull’s Max Verstappen, who went on to snatch both the race victory and his maiden title in dramatic and contentious fashion.
The seven-time world champion has been unable to win a race or challenge for the world championship in the 18 months that have passed, while Verstappen is charging towards a third consecutive drivers’ crown.
1996 world champion Hill has praised Hamilton for the way he has carried himself during a difficult spell and backed the Briton to win an eighth title before he bows out of F1.
“It is admirable the way Lewis kept his chin up after what happened in Abu Dhabi,” Hill told the PA news agency.
“He got back on with the task in hand and he is driving better again this year than he has done before. He is starting to gel with that car now and he has solved some of the problems he faced.
“So I would be amazed if he doesn’t want to go out on a high by winning that eighth title, and he is absolutely motivated by that. He has got that longevity and he looks after himself.
“He needs a competitive car, half-a-chance, and someone like Lewis will rise up to that challenge and find more in himself. At the moment we are seeing a happier Hamilton, and a happy Hamilton is a fast Hamilton.”
38-year-old Hamilton is out of contract at the end of the season but is expected to sign a new deal with Mercedes that would likely see him race into his early 40s.
Hamilton held talks with Mercedes boss Toto Wolff last month amid speculation the deal could be finalised ahead of next week’s British Grand Prix at Silverstone.
A long-term ambassadorial role with Mercedes is believed to be part of Hamilton’s negotiations.
“The talk is that Lewis is finalising a much longer-term deal that goes beyond his racing career,” Hill added.
“The car company itself is involved, so there is a bit more bureaucracy in this deal.”