On a weekend when the celebrated team were set to celebrate their 1000th race in F1, McLaren had a miserable start on Friday as world champ Lando Norris stopped on track in second practice after losing power and Piastri struggled to match the pace of Ferrari, Mercedes and Red Bull.
The Australian was eighth in the first session, and improved only to seventh (1 min 14.088sec) in the afternoon stint, with his best more than a second slower than the pacesetter, Lewis Hamilton (1:13.026), who led home his Ferrari teammate Charles Leclerc by 0.111sec for a one-two.
Local hero Leclerc had also topped the first session (1:13.978), with Hamilton second (1:14.204).
"It felt okay, just not as speedy as we would like, unfortunately," sighed Piastri. "So a bit of a difficult one, we made a bit of progress in FP2 but went from a second-and-a-half off to a second off, so it's been a tough day for us, for sure. Some things to find overnight, definitely.
"We always expected Ferrari to be quick -- and they look very, very quick -- but we were hoping we'd be a fair bit closer."
But Piastri wasn't expecting an overnight transformation. "In today's Formula One, there's never anything you can do to turn the car completely upside down, so we'll try and find something for sure because we need to, but I don't have any great ideas," he said.
For Norris, it was particularly dispiriting. Following sixth place in first practice, he had technical issues early in the second session, with his car stopping on track, forcing him to abandon racing for the day and end with the 19th fastest time.
McLaren's chief designer Rob Marshall said: "We don't know conclusively what the problem was. He had an electrical problem and it shut down, but we've not had enough time to go through the data and find out exactly what's gone wrong. Could be anything, but it's electrical."
Donning a glittering pink race helmet as a nod to Monaco's star-studded reputation, 41-year-old Hamilton, a three-time winner, must be daring to dream a little as it looks his best chance for glory since joining the Italian giants.
Hamilton took his first podium for Ferrari at the second round in China, with a third-placed finish, before being runner-up to Mercedes' Antonelli in Canada a fortnight ago. Now, he'll surely be targeting a record-extending 106th win.
Dominant Mercedes look set for a real challenge, with teenage championship leader Kimi Antonelli only fifth in second practice behind Mercedes teammate George Russell.
Antonelli has won the last four races after George Russell won the season opener in Australia, and tops the drivers' standings with 131 points, 43 ahead of his English teammate.
Overtaking on the legendary street circuit is night on impossible, even with the rule changes instituted this season, so Saturday's qualifying is set to be absolutely crucial to the outcome of Sunday's race.
