The Australian lined up third for Sunday’s race before falling behind Lewis Hamilton to finish fourth after the unfortunate timing of his pitstop shortly before the safety car.
Though he said it “hurts to be so close to a podium,” Piastri said it was promising that both McLaren drivers were able to cling to Verstappen for much of the race.
Given it was his first race with the team’s upgrade package, Piastri said it was “not bad at all”, adding that there’s “still a bit more to come too”.
“I've got the new front wing next weekend, that Lando's had, which is exciting,” he said. “Couple more other bits.
“So, yeah, nice to know that we're fighting here, and we still have a little bit more to come.
“So clearly the upgrades are a massive step forward. I think they're a good step forward over one lap. But the race pace is clearly where we've made a massive jump.
“I think going into the race, I was maybe slightly cautious that we might hit reverse a little bit like we have done previously, but if anything, it was even stronger than Austria, so that was super exciting.
“Yeah, it's hurts a little bit to be P4, when we were looking on for a podium for so long and a bit unlucky with the safety car timing, but I'm just so happy that I'm disappointed with fourth place instead of what we've been disappointed with earlier in the season.”
Asked how it felt to fight Verstappen, Piastri said: “Pretty exciting, to be honest. When I got off the line, and I was like, 'Okay, I've got the best out of everyone here' and had to find somewhere to go, run out of space.
“But I think the more exciting part was being able to hang on to the back of him for a few laps, and even for the rest of the race, it wasn't like he was stupidly quicker than us.
“So that was very exciting, to be genuinely second quickest team today. Exceeded all our expectations. So yeah, nice to be back in front.”
Piastri said it was “definitely” frustrating to lose out on a podium because of the safety car, adding “we were looking so good”.
He added: “We executed everything we could, we were pulling away from the cars behind, all to be one second too far behind pretty much when the safety car came out.
“So it hurts a little bit. But again, I'm so happy that I'm disappointed with P4, as opposed to what it has been earlier in season.”
Additional reporting by Matt Kew
