Button, a winner at Albert Park in three of the last four years, ended up ninth on Sunday while his new Mexican team mate Sergio Perez was unable to get into the final shootout in qualifying and crossed the line in 11th.
It was quite a comedown for the 12-times drivers' and eight-times constructors' champions and a marked decline from the end of last season when they won the last two races.
Button, the 2009 world champion, said winning two points given the state of the car was about as good as it was going to get until there was a major improvement.
"We definitely were not going to get any more points than that so yeah ... we weren't quick but I think we made the right calls considering what condition we had the tyres in after qualifying," he said.
"I think as a team we did a great job this weekend but we are not quick enough and there's a lot of work we need to do to move forward and challenge the front guys. We are a long way off."
McLaren gambled on making significant changes to their car's chassis for this year rather than bring out an evolution of their 2012 challenger, as other teams did in the final year of the V8 engines.
NOT TOO PROUD
The gamble had clearly not paid off in Australia and team principal Martin Whitmarsh, who admitted the team did not yet understand how to get the best out of the car, was asked whether they might consider a return to last year's machine.
"We'll see," he told reporters. "We are not too proud to say when we've got things wrong. We do occasionally and that's just a fact.
"But I think for the time being we've got to try and get some understanding and make sure we do the best job we can to go forward with this car as quickly as we can.
"We think we can work this one out. But if we don't, we'll look at anything."
There is precedent for such a rethink at McLaren, who abandoned the car in development for the 2003 season even before it had a chance to race.
Any switch could not come immediately, with the team racing in Malaysia next weekend, and Button was pinning his hopes on the Sepang track lending a hand.
"We struggled here with the ride," the 33-year-old said. "Everyone's noticed. It's no secret. Hopefully in Malaysia it is a smoother circuit and we'll get rid of those issues and find a bit more performance."
The disappointing race results capped a tough week for the team, who confirmed on Thursday that their long-running and lucrative sponsorship deal with mobile phone company Vodafone would be ending this year.
To compound their misery on Sunday, four of the top five in the race, including winner Kimi Raikkonen and second-placed Fernando Alonso, were former McLaren drivers.
Newly-departed Lewis Hamilton, who finished fifth, has spent much of his time this week saying how happy he has been to join Mercedes after feeling suffocated in his years at McLaren.
"It's been a weekend where we've had to force a smile a few times," said Whitmarsh. "It's been tough. Tough to start a year like this.
"You take some decisions during the winter and sometimes it doesn't come off. It's not pleasant being here if you are used to being a frontrunner."