Piastri had the better start of the two McLaren drivers in Miami, muscling his way past Norris, Carlos Sainz and Sergio Perez after the latter went straight on in the first corner.
In a McLaren that didn't receive all the upgrades that Norris' MCL38 had equipped, Piastri nevertheless showed great pace early on and passed the Ferrari of Charles Leclerc to move up to second behind Max Verstappen.
But it was Norris who vaulted to the top after delaying his only pitstop until a mid-race safety car gave the Briton a free stop, with Norris controlling the race from the restart to take an emphatic maiden win.
In the fight for fourth, Sainz was penalised for contact with Piastri, which forced the Australian to pit for a new front wing and left him down in 13th at the finish.
But while his own race ended in disaster, Stella believes Piastri will take courage from his performance alongside Norris last weekend in a less rapid McLaren ahead of receiving the same specification as Norris in Imola.
"I think Oscar comes out of this weekend even more conscious of his strengths as a driver," Stella said.
"We knew already how fast he is on a single lap, considering that he didn't have the full package. Let me pay proper credit to Oscar, the gap he had to Lando in qualifying is smaller than the difference of the package he had.
"So, he was really pulling off strong performance over a single lap in very difficult conditions like all drivers said with the soft tyres."
Stella added: "His performance in the race was again very strong. Lando said something really nice before, he said by looking at Oscar overtaking a Ferrari, he felt: 'Wow, we are actually there today', so it was a realisation for Lando himself.
"He comes away from this weekend with this sort of conviction, especially in terms of race pace, which is something we wanted to improve having looked at Japan, having looked at China. So, for me, he's in a very strong place."
Stella also praised Piastri for not kicking up a fuss when told Norris would get priority on the full upgrade package, which also included a revised floor and sidepods.
"He has proven once again how strong a team player he is, because clearly when I told him, 'Oscar we are going to give the sidepods and the floor to Lando', he wasn't the happiest in the bottom of his heart," Stella said.
"But at no point he made this decision difficult or asked why. He understood the reasoning and he was immediately supportive, like all the entourage around Oscar."
