The 22-year-old rookie told British reporters at the Japanese Grand Prix that he felt the team were more behind him than the Spaniard after a turbulent season marred by a spying controversy.
"When you are in a relationship with a certain amount of people, you do the best job you can and want to show to everyone that you are the one for the team," said the championship leader.
"In this situation, I was a rookie and he was the two-time world champion coming into the team," said Hamilton. "He is the one that was looked at to bring it home, but eventually I have earned more respect from them.
"And since what's gone on in the last few weeks they've realised who the real people are in the team and who they really should back.
"I feel my bond with the team is even stronger."
McLaren boss Ron Dennis revealed at a 'spy hearing' of the governing FIA in Paris two weeks ago that he and Alonso had not been on speaking terms since a falling out at the Hungarian Grand Prix in early August.
That same hearing, presented with e-mail evidence provided by Alonso, fined McLaren $100 million and stripped them of their constructors' points for having Ferrari technical information in their possession.
ESCAPE SANCTIONS
Alonso, who has been unhappy with McLaren's refusal to give him number one status, shunned the hearing while Hamilton attended. His lawyer also made a plea for the drivers to escape sanctions.
"I want to win it fair and square. Not once have I approached the team members and asked to be favoured," said Hamilton of a title battle that could take a decisive twist in Fuji on Sunday.
"It is just not something I have done at any team, asking for better equipment."
Hamilton said after the controversial Monaco Grand Prix one-two, when the Briton complained that McLaren were treating him as a number two driver, the team had been scrupulously fair.
"After Monaco they didn't know what to do with the strategy so they made us equal and gave us equal fuel loads and whoever outqualifies the other has done the better job," he said.
"I want to win it the right way. The best feeling ever is when you know you have won and you have beaten someone as talented as he is with the exact same equipment and exactly the same opportunity."
Hamilton, Formula One's first black driver who has been supported by McLaren for more than a decade, said he had been forced to change his opinion of Alonso.
"You try to understand these people but then the whole idea of what sort of person they are is completely miles out of the ball park," he said.
"He is not the person I imagined him to be, but that's the way it is."
