Last year's runner-up to Red Bull has now slipped behind Aston Martin and Mercedes to fourth in the constructors' championship ahead of this weekend's Spanish Grand Prix.
Unlike rivals who chose to bring major upgrade packages anyway to the unrepresentative Monaco lap following the cancellation of the Emilia Romagna GP, Ferrari instead opted to hold off its bodywork upgrades scheduled for Imola until the coming Barcelona event.
But by not delaying, Aston Martin's Fernando Alonso was a representative second in Monaco while the revised Alpine ran to third in the hands of Esteban Ocon. Meanwhile, the Mercedes drivers were content with the performance of upgrades as they ran to a 4-5 finish.
Ferrari's top finisher in the principality was home hero Charles Leclerc, who recorded sixth as a legacy of a five-place grid penalty for blocking Lando Norris in qualifying.
Speaking to select media, including Motorsport.com, Vasseur said it "would be a mistake to compare approach" after competitors who pressed on with upgraded cars outscored Ferrari in Monaco.
But the newly appointed team boss stressed that the factory was "pushing like hell" to bring forward updates to the SF-23 machine since the outfit was "not happy" with results.
He said: "We are pushing like hell at the factory to bring an update as quick as possible because we are not happy.
"I think the results we have today are not the target and we want to do better. We will continue to develop in any case."
Vasseur, who said he was always "expecting hard work" during the early part of his Maranello tenure, reckoned he had not set any performance targets for Ferrari.
Instead, he would consider progress on a day-to-day basis, saying: "The target is not in terms of position.
"The target and the important mindset that I have to push for is to do a better job tomorrow than today.
"As soon as we are able to analyse that we have weakness on the car, on the approach of the team or in the garage, we put all of our effort to fix it."
Vasseur cited Ferrari having rehearsed "thousands" of practice pitstops over the winter to address one weak spot of 2022. He is now calling on "every single employee" to help Ferrari's performance.
"It would be a mistake to imagine the lack of performance is coming from just the [aero]," he continued.
"Performance is coming from everywhere: the capacity to produce parts quickly, the strategy, the pit wall, the mechanics, the pitstops, the reliability.
"Every single employee of the company is a performance contributor."
