The Scuderia emerged as the nearest challenger to Red Bull at the start of the second ground-effects F1 era and finished 2022 as the championship runner-up.
But it has now dropped behind Mercedes and Aston Martin to fourth in the 2023 constructors' standings ahead of the second part of the campaign.
Alongside this performance drop-off, criticism remains over the team's strategy calls and pitstop execution, as per last year.
With a 312-point deficit to Red Bull ahead of the Dutch Grand Prix this weekend, Maranello boss Vasseur says Ferrari must address "every single pillar of performance".
Speaking to select media before travelling to Zandvoort, Vasseur said: "If you look at the numbers, it's quite difficult to imagine that we could be champion on the team and driver championship [this year].
"But we need to keep the same mindset to try to get the best on everything that we can and not to be focused on the championship.
"We have to improve the package, but we also have to improve what we are doing on track and to try to get the best from the package that we have. It's clear we have to be focused.
"But I don't want to fix a target to say that we have do 'this' or 'this'. As long as we have room for improvement, we have to put some focus on this.
"It's clear that on every single topic and every single pillar of the performance, we have to make a step forward."
Ferrari has lost head of vehicle concept David Sanchez to McLaren, while racing director Laurent Mekies has now left the organisation ahead of becoming AlphaTauri team principal.
In return, Ferrari has hired Mercedes performance director Loic Serra. But he will not start in Italy until 2025.
In response, Vasseur has said Ferrari is "recruiting a lot" amid an ongoing internal restructuring.
He continued: "It's not the result that we are expecting and, as every single team on the grid, we need to be in a continuous improvement mindset, and we are recruiting a lot.
"We change already some internal organisation positions, but we are moving forward."
He added that this drive to improve meant Ferrari was undertaking a never-ending process: "The most difficult part of the job is to understand what is going well and what is going wrong and where we can improve.
"We are working a lot to try get the last couple of tenths that are missing today. But we are in the middle of the process and it's a non-end process."
