The Briton said instead improved correlation between simulations and on-track experience was the main cause for optimism, even if that remains more of a long-term fix.
The team had said resolving its correlation problems was its chief priority in the build-up to this weekend's Spanish Grand Prix.
"Its great that we're able to turn things around so quickly in terms of bringing parts to the circuit, but we're still a hell of a long way off the pace," Button said of the updates.
"There are some positives to the parts, but some areas we need to improve on - areas I didn't think we would have to.
"We haven't slipped back, we've made improvements but I think everyone has.
"The important thing is that the correlation much better now, which is a positive, definitely for the future.
"I think [on Sunday] you'll see four teams that are very competitive at the front. I don't think we'll be one of them but I think we'll be just behind hopefully."
Button said the mixed conditions of FP1, and the need to focus on long runs to ascertain how the tyres will behave, hampered McLaren's ability to test new parts.
"The problem is we've hardly tested: its not perfect conditions, [and then] its basically been doing long runs seeing what the tyres will do," he explained.
"We still don't have the outright pace of the quick guys as everyone is moving forward; we need a big chunk and I'm not sure we have that.
"I think we can improve overnight, but we're not there yet."
While Button was not able to test McLaren's new front wing, team-mate Sergio Perez bolted it on for the final 15 minutes but said evaluating its effectiveness was nigh on impossible.
Asked whether tyres and varying fuel loads had complicated the picture, he said: "Exactly. I tried the front wing, but it was pretty difficult to draw any conclusions.
"It was a very intense session, not the kind of day we were hoping to have but a lot of information for the engineers."
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