The Briton could only manage 17th on the grid, three seconds down on the pole time of Mercedes' Lewis Hamilton - while team mate Kevin Magnussen was six tenths of a second down the road in 18th. It was McLaren's worst qualifying performance since a rain-affected session in Malaysia in 2010.
"This level of performance wasn't a surprise for us: we knew from winter testing that the pace wasn't there, so we knew we weren't going to be competitive here," Button said.
"However, there's a good feeling about the car - I know we're so far off, but the basic car is there beneath me, and we're adding to our experience and learning with every lap we do.
"And that's really impressed me - we've gone through our first race weekend together, and we've managed to solve each issue that's confronted us. There's just a lot of work needed to add power and downforce - but this is an important car for the future of McLaren-Honda."
Button also warned against expecting a change of fortunes in Sunday's race, adding: "It's going to be a really difficult race for us. We haven't done a race distance yet, and my longest run is 12 laps - but we want to do the best we can because there's so much learning to be had."
Honda's chief officer of motorsport Yasuhisa Arai said McLaren's sizeable pace deficit to the rest of the field stemmed in part from a decision to adopt conservative engine maps for Australia, but admitted there is also a lot of work needed to get back to the front of the grid.
"First of all, I must thank both drivers for maintaining their faith and determination - we're not where we want to be, but their input and positivity are really helping the whole team push forward," he said.
"Unfortunately, today's higher temperatures didn't help the conservative data mapping settings that we chose to run this weekend. From the outset, we took the decision not to gamble any engines away in the opening race, so there'll be more to come from us.
"McLaren and Honda have come a long way together since the beginning of this project, but we still have a long way to go. However, I'm sure that we'll continue to make progress - and that first step starts in the race tomorrow."