McLaren endured a tough start to the season in free practice at Albert Park, as both of its drivers were more than two seconds off the pace set by Sebastian Vettel.
Team boss Martin Whitmarsh suggested last week that targets were low going into the season-opener, and Button said in the paddock on Friday that McLaren has a lot of work to do.
"The way things have gone today, I think points would be very positive," said the 2009 world champion.
"We're obviously not quick. The feeling is not good with the car, so we've got a lot of homework."
Button admitted that he knew the MP4-28 was off the pace in testing, but he thinks the gap in Australia has been exaggerated by the team not getting the most out of the car yet.
"After the last test we knew we didn't have the pace," he said. "We couldn't have got anywhere near the laptimes the other guys were doing in testing.
"We were over a second off, and it's even more here. And that's not right.
"You always hope that when you get to the first race and it's a bit warmer that things will turn your way, but at the moment they haven't.
"We have quite a few weaknesses with the car. Ride is a lot worse than we expected, so we have been working with that today trying to find a direction.
"It's not easy at the moment but I'm sure we can do a better job than we have so far."
Button said that it was key for the team to work out overnight "if the car is doing what we think it's doing", and his new-team mate Sergio Perez added that the car was difficult to understand on track.
"The car is so unpredictable," said the Mexican. "It's not only doing one thing, it's doing so many things that it will be very difficult for us to set up.
"The car is quite inconsistent through the corners. It's quite difficult to drive and to extract the maximum performance.
"It will be very hard to get some points [this weekend], but anything can happen. We could have some surprises with the weather."
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