Norris and Piastri started third and fourth on the grid but the team chose intermediate tyres for both cars while most of the field went with slicks in cold and slippery conditions.
The decision briefly looked promising when Norris stormed into the lead but the rain had stopped before the start and both cars were forced into early pitstops as the track dried out.
"Unfortunately for us, it stopped raining as the formation lap started, basically," Piastri told Sky TV.
"So, yeah, just one of those things where had it rained a little bit more, we would have looked like heroes. But it didn't, so we looked like idiots."
Team principal Andrea Stella said the call should be judged based on the information available at the time, rather than just on the outcome.
"The rain stopping pretty much after the five-minute signal, and then the double formation lap handed a clear penalty to starting on inters," he told reporters.
"With the rain lasting for a few more minutes, and the race start happening at the right time, we could have seen a big cut starting on the right tyres."
McLaren's problems continued after the tyre gamble failed. Piastri, trying to recover, locked up and collided with Albon on lap 15, putting the Williams driver out of the race.
"I wasn't trying to overtake him. I just locked up, and that was it," said the apologetic Australian, who was handed a 10-second penalty and finished 11th.
Stella said the penalty was deserved and described the incident as a misjudgement.
Norris, Stella said, had made an earlier stop because of overheating and the need to clean the radiators but said it was a seperate issue to gearbox problem that forced him out of the race.
McLaren, the reigning constructors' champions, finished without a point on a day when championship leader Kimi Antonelli won his fourth straight race for Mercedes.
Norris is in fifth place in the drivers' standings 73 points behind the Italian teenager, while Piastri is sixth a further 10 points back.
"Today was not our day," Stella said.
