Piastri damaged the right side of his wing when he touched Gasly's Alpine at the exit of Turn 2, and just a few hundred metres later debris flew off the Australian's car.
In a bizarre coincidence, his McLaren team-mate Lando Norris hit the debris from Piastri's car and also had to make an early stop.
Piastri had no option but to pit at the end of the first lap, while Norris initially appeared to have got away without too much damage.
However, on the second lap, his MCL60 became visibly tricky to drive and he reported "something's not right with the front end, I have too much understeer."
He was called in at the end of the lap leaving the two McLarens at the tail of the field. They eventually finished 15th and 17th, with Piastri ahead.
Piastri admitted he hadn't expected the contact with Gasly to be so costly.
"I haven't seen it yet, I'm not 100% sure," said the Australian when asked what happened.
"I think it was really just one of those lap one, Turn 1 incidents. The contact felt really small. So I was honestly quite surprised to have damage."
McLaren boss Andrea Stella said his team will take the double misfortune "on the chin".
"We looked at the replay, first of all from Oscar's on-board, to check whether there's something to learn there for the next time," Stella told Motorsport.com.
"I think Oscar just was as prudent as he can be, like looking from Gasly's on-board, it looks like he just lost control, drifted a little bit, and touched Oscar front wing.
"So I would almost dare to say that I would classify it as one of those unfortunate situations.
"Even more unfortunate though is that Lando hit the debris coming off Oscar's front wing.
"So we had both cars having to change the front wing. Clearly in the data, it was a massive loss of downforce, it would not be possible to continue like that.
"And we were not helped by the fact that there was no safety car. So we needed to take the heat of the stop of the first lap, plus the front wing change, plus no safety car.
"So we take these things to the chin. We are racers, we don't give up. We just move on to the next race."
