Button and team-mate Sergio Perez were trying revised bodywork in Friday practice at the Spanish Grand Prix.
Button said: "It's going to be quite a big gap to the front. There are some areas we need to work on.
"Everyone is improving so you need to make a bigger step than them and I don't think we've done that."
Button was 12th fastest in the second session, about 1.5 seconds off the pace-setting Red Bull of world champion Sebastian Vettel.
Perez was 13th, half a second slower than his team-mate.
McLaren revealed on Wednesday that the team had been afflicted by a problem that meant the car was not responding on the track in the way simulations in the wind tunnel suggested it should.
Button said the team had established that this was "much better" but added: "We still need more. Everyone always wants more performance and that's what we're working on now."
He said: "It's great we are able to get some parts on the car. There are some positives with the balance but also some areas that are not as good as I'd hoped, areas I didn't think we'd have to work on."
Perez also tried a new front wing, but he said that he was unable to draw immediate conclusions about its effectiveness because he ran a different set of tyres with it.
The Mexican admitted that McLaren no longer had any chance of battling for the championship.
"At the moment it is not realistic to think we are going to be fighting for the title," Perez said. "It is the fifth race and we are two seconds off the pace. We are in a similar situation to three weeks ago so points is the target."
Jenson Button says McLaren "are still a hell of a long way off the pace" despite an upgrade aimed at improving their Formula 1 car.