Even after the addition of a technical directive banning the use of engine 'party modes' ahead of last weekend's Italian Grand Prix, Red Bull has struggled to match the pace of Mercedes over a single lap.
However, Verstappen claims to be far happier at Mugello than he was one week ago.
"Luckily from the start [of practice] the car was in a good window - night-and-day difference compared to Monza. Of course, at Monza downforce levels and everything are very different," said the Dutchman.
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"I felt very happy in the car. It was all about fine-tuning things and trying to do things better, but overall, a very positive weekend so far.
"We were reasonably close to them in qualifying, so we can be happy with that. In Q3, I expected more, but my first lap wasn't the best lap of my life - it wasn't bad - but it wasn't the best.
"And then I wanted to push a bit more in the second, I was close to Lewis, a bit more in the tow, but I think the wind picked up, so the track was just a bit slower. I managed to improve a bit more so it meant there was a little bit more in it, but not four-tenths.
"I didn't expect to beat them in qualifying, but I'm pleased we are back in third, and not too far away."
In the sister Red Bull, Alex Albon equalled his career best qualifying result and will line up fourth alongside Verstappen.
With a long drag to turn one, Verstappen is hoping both he and Albon will benefit from a tow from the Mercedes cars, putting them in a position to fight in the opening exchanges.
Verstappen added: "They [Mercedes] have quite decent top speed this year, so that's quite good around here.
"It won't be easy to pass, but at least the track, the last few corners they are wide and long, so you can do a few different lines.
"So it's all going to depend on whether you have the pace to follow, and second, tyre degradation."
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