The Australian stepped up to a McLaren race seat for 2023 after spending last year as Alpine reserve and test driver.
With McLaren's car not being as quick as the team had hoped, it has not been the smoothest of rookie campaigns for Piastri, but he feels he is making progress.
And he has singled out the assistance that Webber, a veteran of 217 grands prix, is giving him – both in terms of how he helped prepare him for the challenges of F1, but also in making the most of dealing with the team.
"Coming into this year I think my personality was quite relaxed, maybe a little bit too relaxed for Mark's liking at some points," said Piastri in an interview with Motorsport.com.
"His advice was to not underestimate the challenge of Formula 1 and how big of a step up it is, not just from the cars but from everything: the amount of people you need to interact with, the media commitments, and the sponsor commitments. It's all much higher than before.
"I think having him reminding me of that before the season started was nice, so not to be shocked when I arrived. That's probably been the biggest thing.
"But he's very helpful with small driving tips here and there as well, and sometimes thinking of questions for the engineers that don't even come to my head at the moment.
"He's still very sharp. He thinks like a racing driver still and is always trying to get the best out of me."
Piastri said that it was hugely comforting being able to call upon the advice of someone like Webber, who he has worked with for many years now.
"Mark has been great," added Piastri. "Even before I got into Formula 1, he was very helpful managing me in F3 and F2.
"Now in F1, he knows a lot of people in the paddock and had a successful career himself, so he knows what it takes from a drivers' point of view, but also from a team point of view and everything else as well. He knows everything that goes into it.
"So, he's been great so far. I'm sure he will continue to be in the future as well. It's really comforting having somebody who's been in my position before, guiding me through all of this."
Piastri believes that one of the aspects of his driving that he needs to improve is getting up to speed much quicker on a race weekend.
He feels he leaves himself with too much of a step to make in qualifying, which often leaves him falling short of team-mate Lando Norris.
"I think by the time it comes to qualifying, especially in the last few events, it's been quite comparable to Lando," he explained.
"But in Monaco for example I was six or seven tenths off through all of practice. Going into qualifying with that deficit is not the best for your confidence.
"And also, in terms of trying to find the time, others are finding little bits in a couple of corners, and you end up with the need to find quite a lot of time, which sometimes it's not that easy to find.
"So, I think if I can get to that stage earlier in the weekend, it'll make life a bit easier for myself.
"It will also make life a bit easier for the engineers trying to set up the car as well, because there's me trying to find a lot of the time and then they are trying to find the time too. So that's probably my biggest focus at the moment."
