Mansell, Brundle, predict more struggle for Button
While Lewis Hamilton finished on the Bahrain podium in the sister McLaren, Button's car number one was 20 seconds down the road in seventh place, and he admitted afterwards that he overly nursed his tires.
In his post-race scrum with British newspaper reporters, the 30-year-old was asked if Hamilton, 25, had won 'round one' of the new British battle.
"If you want to write that, you can write that," Button answered.
"It's a fact that Lewis finished in front of me. He did a better job today," he added.
But Button, who has switched from the Brawn team that in 2010 has become Mercedes GP, insists he was stuck in traffic on Sunday having qualified four places behind Hamilton.
"My pace was very good. But Lewis is an exceptional driver," he said.
"It would be difficult for any driver to come in and be quicker than someone like Lewis but I am working hard to improve myself in qualifying, to find a car that suits in qualifying, and I am happy with the progress I am making and the team is making," said Button.
1992 world champion Nigel Mansell, who was in Bahrain at the weekend, thinks Button will have to get used to being behind Hamilton for the time being.
"I give Lewis the edge for the first six races," said the 56-year-old.
"But Jenson will settle down and compete very strongly," added Mansell.
Martin Brundle, who is tipped to become Hamilton's new manager after being spotted in meetings with the 2008 world champion in Bahrain, thinks Button has a mountain to climb.
"Button has entered Hamilton's domain declaring he needs a new challenge — I presume the alternatives were climbing Everest or swimming the Pacific Ocean," the former McLaren driver wrote in the Times.