The Australian followed ninth-placed team-mate Lando Norris over the line to record a double points finish for the team in a performance that passed without major error.
That was despite the treacherous wet conditions late on that notably caught out more experienced operators Sergio Perez and George Russell.
Piastri reckoned he survived the 78 laps without so much as grazing the barriers, although admitted he came close when chatting over team radio.
He said: “I don't think there was any touches, but some very close moments - especially on the slicks.
“One time, I keyed up the radio to talk and almost put it in the wall mid-sentence.
“I won't do that next time! But a few close calls.”
PLUS: Monaco Grand Prix Driver Ratings 2023
Piastri, who called Monaco his most difficult F1 weekend to date, added that he had used the blue flags to allow leader Verstappen by, only to follow the Red Bull driver to rapidly boost his experience of driving an F1 car in slippery conditions.
“Having Max right in front of me was actually quite useful in some ways, because that was my first time on slicks on a rainy track in an F1 car,” Piastri said.
“Having Max there, I obviously knew that if there's going to be anyone, that's probably going to be OK.”
Asked by Autosport if he had any trouble keeping up with the dominant RB19 when grip was reduced, Piastri reckoned: “When it was raining on the slicks, understandably, he was being very cautious. I could keep with him quite well there.
“Even when we came out on inters, I could keep with him quite well.
“Once the track dried up and he got a bit more comfortable, then he was a fair bit quicker.
“But initially, I was managing to keep behind him, which is the best I've been able to say that. So, it was nice.”
McLaren team principal Andrea Stella reckoned his driver had satisfied the ‘most optimistic’ plan the crew could have envisaged.
He said: “In the race, there was, if anything, another element of building the racecraft, which is a racing situation in which you need to first, keep it on track with no mistakes on dry tyres on a track that is getting wet. Quite wet in some places.
“Then finding the rhythm in between the walls on intermediate tyres. So, to be honest, for being a rookie, this is going to be the most optimistic plan we could anticipate for Oscar.”
