McLaren's new team boss Eric Boullier said Magnussen's was "one of the finest performances by a formula one rookie in living memory".
F1's oldest driver last year was Mark Webber, and although still competitive he explained in Melbourne at the weekend that he chose to retire as he realised his performance curve was dipping.
"I've had a great career," Button is quoted by the Telegraph, "but for me it's definitely not near the end.
"People have said 'Ah, he's 34, end of your contract, what are you going to do at the end of this year?' It's going to be the same as any other year," the Briton insisted.
"It doesn't matter if you've got a contract, if a team don't think you're doing a good enough job then they'll get rid of you, and if you're doing a great job they'll want you for 10 years more."
Button said he has not considered what he would do if his only option would be to leave McLaren and join a smaller team.
"I'm here at McLaren and that's where I'm happy to be. I'm not going to get worried either way," he insisted.
The situation could, however, ramp up the tension between Button and the 13 years younger Magnussen this year, but Boullier insisted he is not worried.
"I think you should ask that question to Mercedes or Ferrari," he is quoted by Germany's Auto Motor und Sport.
"For us there is no problem."