Hamilton, the 2008 champion, formed a dream team at McLaren with the 2009 title-winner Button for three seasons from 2010 to 2012.
The duo scored 18 wins during that period - Hamilton 10, Button with eight - when Sebastian Vettel and Red Bull dominated.
Button feels with a clear structure at McLaren of a number one and two driver, as was seemingly the case at Red Bull, then either he or Hamilton could have won a second title, although racing on an equal footing was part of the attraction of being with the team.
“The only reason why Lewis or myself didn’t win the world championship was that we kept taking wins off each other," said Button, on a podcast with 2016 champion Nico Rosberg.
“If it was the Sebastian Vettel-Mark Webber situation, one of us might have won the world championship."
When Button left Brawn to join McLaren at the end of 2009, the move was viewed as high risk as at that time McLaren was built around Hamilton.
"If we’re performing well as a driver you get to choose kind of where you want to be and where you think is the right place," explained Button.
“It’s like when I went to McLaren after Brawn, it was the right decision. I know that you were at Mercedes, but it was the right decision to go to McLaren.
“They should have ended the year with a win but they had a failure with Lewis and when I got there, it was a great team.
"So it was the right call, but then three years later, it wasn’t the right call and Mercedes was the right place to be.”
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