Piastri had a frustrating time in the opener in Bahrain, admitting to mistakes in qualifying that cost him a shot at Q2, and then suffering an electrical issue early in the race.
But in Jeddah he made Q3 and qualified ninth on a day when team-mate Lando Norris damaged his car early in Q1.
In the race both drivers were compromised by early stops for front wing damage. Piastri eventually finished two spots ahead of Norris in 15th, the pair having run different tyre strategies.
Stella praised Piastri’s improving form after the difficult Jeddah race, while acknowledging that the team has to give its drivers a better car.
“We have seen really strong progress by Oscar,” Stella told Motorsport.com. “Obviously, Lando is a complete certainty. So we know that Lando is there.
“So there's some positives, but for me the message stays the same. We need to work hard to improve the car and go back racing where we should belong.”
Asked if Piastri had made a big step over the Jeddah weekend, Stella suggested it was more a case of a gradual improvement every time he drives the car.
“I wouldn't say that he took a big step,” said the Italian. “For me it's going steady progress session-by-session.
“But like if you look back, already in FP1 he was a little bit more competitive than Bahrain, then FP2 closer, then FP3 pretty much a match for Lando, capitalising in qualifying, and then very strong in the race.
“For me, I see more the sense of constant progression, which is ultimately the plan that we have with Oscar.”
Stella acknowledged the Australian GP is going to be a big weekend for Piastri on his home debut, but he downplayed the suggestion that the team will have to keep the local hero in a bubble in order to reduce the demands on him.
“He is a very calm guy, I think he will be able to keep himself in the bubble,” Stella explained. “But certainly we'll have to make sure that he can stay focused on racing, and he can stay focused on keeping up with this exceptional rate of development session after session.”
Regarding prospects for the MCL60 in Melbourne, he said: “As a track in in terms of tarmac grip, speed of the corners, I would say it should be more similar to Saudi then Bahrain.
“So we look forward to that place in terms of being able again to challenge for Q3, and challenge for good points.”