Piastri qualified on the front row for Sunday’s race but was bumped to fifth following a post-session grid penalty for impeding Kevin Magnussen.
The Australian was caught out in the Tamburello chicane after he was not given any warning of the approaching Haas until it was too late.
Piastri raced his way forward from fifth to fourth in the race but was powerless to progress further around a circuit that is notoriously difficult to pass on.
Max Verstappen won the race from pole position, holding off Lando Norris who started second.
Norris had qualified third, but was promoted one spot on the grid courtesy of Piastri’s penalty.
“I think Oscar pushed as much as he could in this race,” Stella said.
“I am saying this because looking at his data and speaking to his tyre engineers that he is pushing at the limit at the end, so Oscar I think he went flatout and I don’t think he could have gone any faster.
“I think in managing the budget overall, Leclerc was a little bit more than Oscar and he could retain the podium.”
Having cleared Sainz following the pit stop cycle, Piastri caught and harried Leclerc for third.
However, his challenge faded as he used the best of the tyres and ultimately drifted six seconds back from the Ferrari at the chequered flag.
“It’s a little bit of a shame for Oscar because the performance he deployed yesterday, he had the performance over the weekend to score a podium,” Stella noted.
“We take the blame for that because the reason he got the penalty was impeding and that was to do with our operations, it doesn’t have to do with Oscar making any mistake at all, it was a situation created by the team.
“But I am sure Oscar will have opportunities in the future.”
In Imola, Piastri had all the latest upgrades, the Emilia Romagna Grand Prix confirmation of McLaren’s increased pace as it proved a match for both Red Bull Racing and Ferrari over the course of the weekend.
“It is a confirmation in Miami and in Imola, which are they are definitely two different positions on the spectrum of the circuits we visit, but the thing with Monaco is it is on the limit of the track characteristics,” Stella explained, noting this weekend’s Monaco Grand Prix.
“Last year, if I’m not wrong, think what happened to Alpine. They were mega in Monaco.
“And that’s Monaco. Sometimes the car works really well, your drivers are really in the groove.
“So I would suspend the judgement for the moment, be prepared as possible with the race operations and have some track specific upgrades as well.
“We will take some new parts to Monaco, which are track specific for the maximum downforce configuration, and hopefully they will help us staying in the quest.”