Hamilton is 33 points behind the German with 100 available in the last four races, the first of which is the US Grand Prix in Austin, Texas on Sunday.
The Briton said: "You can't win them all. Look at the great champions who lost titles. It's part of the game.
"I'm going to give it everything I've got and everything is possible."
Should he lose, Hamilton said "life would move on" and he would hopefully "come back stronger".
The 31-year-old has won three of the four US Grands Prix held at the Circuit of the Americas since the event made its debut in 2012, and said he was "excited" about the weekend.
Hamilton pointed out he has the worst of the reliability issues at Mercedes this year, with engine problems affecting his results at four separate races, including a failure while leading in Malaysia earlier this month.
Without these problems, Hamilton would be leading the championship rather than trailing Rosberg, who has so far had only one reliability issue affect his points total, costing him three points at the British Grand Prix.
Hamilton said: "We have always had close battles. If all things were equal, there would be a certain result.
"This year has been a little different in terms of how our performances have been mechanically and there is nothing I can do about that.
"When the car has been good, I have often done the job with it and there has been a few, especially in the first few seconds of the race, when I have not done that well. But that's motor racing."
Hamilton has had five bad starts this year that have cost him positions, compared to three for Rosberg.
He said he had been working on the problem again with Mercedes before coming to Austin.
"It has been an ongoing thing all year long - perhaps more work than in other areas," he said. "I was working on it at the factory last week and we hope we have a better formula this weekend."
Hamilton's behaviour in the pre-race news conference on Thursday was very different from his controversial performance in the same event in Japan two weeks ago.
In Suzuka, he was relatively disengaged from the process, referring journalists to his social media outlets for answers to questions, and spent time posting pictures on Snapchat of himself and fellow driver Carlos Sainz with cartoon animal features.
In Austin, he was polite and concentrated and gave long, considered, thoughtful answers - much more his normal self.
He also explained why some journalists had been blocked from following him on Twitter, saying he had only recently found out about it.
"I don't manage every single part of my social media," Hamilton said. "I have a couple of people doing it for me. It was a blocking spree. I don't even have the app on my phone."
He said the general approach was for people to be blocked if they said something negative - and those affected had not just been journalists.
Ferrari driver Sebastian Vettel said Hamilton had every chance of ending the year with a fourth title.
Asked if it was realistic for Hamilton to catch Rosberg, the four-time champion said: "Of course. He is quick enough and there are enough races.
"I am sure he will go for it. Four races is a lot of laps to do, a lot of things that can happen. It is only over when it's over."
Subscribe to the BBC Sport newsletter to get our pick of news, features and video sent to your inbox.
Lewis Hamilton says he will "take it like a man" if he loses this year's Formula 1 title to Mercedes team-mate Nico Rosberg.