The 2009 world champion managed just 52 laps and the fifth fastest time during the second day of this week's final pre-season test at the Sakhir circuit, as a gearbox problem limited the MP4-29's running.
Button said McLaren was still running its car in "launch specification" and would need to find more speed during the final two days of testing in order to challenge at the front in Melbourne.
"We've got a lot of work to do still," said Button. "I think the basic car is good but we're still waiting for our upgrades.
"The first race package will hopefully move us a bit closer to some of the other cars because we are behind quite a few teams at the moment, probably more than we expected, but I'm not worried.
"It definitely has potential this car. It has a very good feel about it.
"We have a very good understanding of the power unit and how to use the ERS, but at the moment outright pace is something we need to work on.
"At the moment we're not quick enough, but that's always going to be the case when you've still got the launch car."
Button hinted that McLaren might not introduce its full race upgrade package until after the final Bahrain test has finished.
"There will be some parts this test, but I'm not sure all of it," he added.
"There's a lot to put on this car for the first race and hopefully that will be enough to put us into the fight in Melbourne."