The initial laptime gap compared to the same Jerez test last winter was a disastrous 10 seconds, but McLaren rookie Kevin Magnussen ultimately got the gap down to under 6 seconds.
Nonetheless, GP2 - with unchanged technical specifications - will come close in 2014.
"They will be a lot closer on certain circuits," 2009 world champion Button agreed.
"We'll be quicker, but not that much quicker."
However, the McLaren driver thinks that with F1 set to embark on a steep and speedy development curve with the clean-sheet regulations, the Jerez cars will be substantially faster by the time the season begins in Australia.
"And three races in there will be another chunk in terms of laptime," said Button.
"By the end of the year we might not be that far off (2013 pace), maybe a couple of seconds, which will be pretty good when we get a real handle on where we are."
Some of the extra laptime, Button explained, is due to Pirelli's new, harder and more durable tyres.
"We think they are half a second slower," he said.
"The cars are also heavier, about one to 1.2 seconds through weight, so that's 1.6, 1.8 seconds already from those two changes."