McLaren looked good in Saturday’s FP3 session after overnight changes, with Lando Norris seventh and Piastri backing him up in eighth.
Norris’s qualifying session was ruined by contact with the wall in Q1 but Piastri made it through to Q3 and earned a solid ninth place.
That will translate into eighth on the final grid for his second F1 start thanks to a penalty for Charles Leclerc.
“I think every time I've jumped in the car I feel like I'm getting more and more comfortable,” said the Australian. “I think compared to Bahrain, I don't think I did anything massively differently or change anything.
“It just was all coming together better and better, and no mistakes today. It's still incredibly tight. But I was at the right end of the of the pack this time. So I just felt like I put everything together much better today. And it made a lot of difference."
Piastri admitted that he was careful to build up his speed at the tricky Jeddah street circuit, despite knowing it from his F2 days.
"I think the first few laps in practice on Friday, everything was coming a bit quicker than I remembered from F2!,” he said when asked by Motorsport.com if he had been pacing himself.
“So that took a bit of getting used to, obviously. I think more than anything just getting more comfortable with the car has been beneficial. I feel like if you can get yourself comfortable with the car, then no matter what track you go to, it makes life easier.
“Even from Bahrain to here it feels like I've made a good step, and throughout this weekend and overnight. I think this morning was a good session, and obviously qualifying went well as well. So yeah, just building up into it.
“I think a bit of track knowledge maybe helps, but in saying that I've done plenty more laps of Bahrain than I have here! So I don't really think it was that, I think it's just getting more and more comfortable with the car.”
Asked if the car’s one lap pace is better than expected, he said: "I think our just general pace seems a bit stronger. I don't think we really expected one lap to be better than our race pace, if anything Friday was almost the opposite to an extent.
“So we'll see what we've got on Sunday. But yeah, I think when we've got high grip, when we take the fuel out, I think for everyone the car feels a bit better.
“But for us it was good. I think what we did overnight really helped quite a lot. Even if it was not revolutionary, I think we were much more optimistic after P3 than we were at this point last night.
“So just those small margins again, really, really make a difference. And on Sunday, it'll be a close race I'm sure. A lot of other cars have got different strengths to us. So we'll see how that plays out tomorrow.”
Piastri conceded that the team can now be more optimistic about what might be achievable this year.
"Yeah, I think so,” he said. “It's just so tight. Even in Q1, I think the difference between being in the top 10, I think where I was, and being out, was like two tenths.
“So you make a small mistake, or a couple of small mistakes, and it looks like a complete disaster. And you put a really good lap together, and you look like a hero.
“So we've really got to tackle those really small margins, which I think we're doing a very good job of. And obviously, we've got some upgrades in the pipeline throughout the course of the year that will help, but I'm sure everyone else will, as well.
“And just managing to eke a little bit more out everywhere we can, especially with the field so tight as it is now, is going to make the difference."
