Piastri missed out on top spot by an agonising 0.01s at the end of the three-part session.
Max Verstappen claimed a surprise pole for Red Bull, the second time the Dutchman has defied the odds in three races.
“There wasn’t much more left in that lap,” Piastri said.
“I’m happy with the job I did.
“I think it was playing catch-up a little bit through the first part of qualifying and then that last lap felt more or less like the best I could have done.”
Piastri had been the only one of the remaining drivers to record a lap before Lando Norris crashed in the early stages of Qualifying 3.
Norris ran deep at Turn 4, climbing the exit kerb which speared him across the track and into the barrier.
The resultant red flag was shown just seconds after Piastri flashed across the line with an early banker lap.
Verstappen mugs McLaren as Norris crashes in Saudi Arabian GP Qualifying
Verstappen’s time came after an unusual approach following Norris’ red flag.
Without a time on the board, a time running out, Red Bull opted to send the four-time world champion out with enough fuel for two timed runs, with effectively a racing stop for new tyres in the middle.
It was an approach McLaren considered but ultimately opted against for Piastri.
“We spoke about it, yes, but decided against it,” he admitted.
“Considering I had a lap on the board, I didn’t need to put another one on.
“It was going to be extremely tight. [Verstappen] had to fuel for the whole run.
“That first lap on used tyres with a bit more fuel, you’re weighing up how much you’re learning versus how much it puts you off.
“When you don’t have a lap on the board, it’s a very different scenario.
“We decided to go for that single lap at the end, and I think for us, it was the right decision.
“I made a bit of a mistake on the first lap and managed to get through [Turn 4] much better on the second attempt,” he added.
“When you need one hundredth, you can think of a few places.
“It was a good lap that I was happy with.
“That was pretty much all we had.”
The result is, in many regards, a repeat of qualifying at the Japanese Grand Prix, where Verstappen pulled out a lap against the odds to seize pole.
On that occasion, he converted it into victory after absorbing pressure from both Piastri and Norris throughout the race.
While starting from pole offers the potential for Verstappen to repeat that performance in Jeddah, the circuit itself will make his task more difficult.
“Suzuka is not a completely different layout to somewhere like here with a lot of high-speed corners, so it kind of makes sense to me at least that they’re a bit more competitive, and we’ll see if that translates to the race tomorrow,” Piastri noted.
“I’m feeling confident in what we’ve got.
“There’s a lot of DRS zones around here, which is a nice difference to Suzuka.
“So, yeah, let’s see if we can make some progress.”
While Piastri starts second, Norris’ crash locked him into 10th on the grid.
The McLaren pair are separated by just three points at the top of the drivers’ championship, headed by Norris, going into Sunday’s race.
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