The SF-23 has been quick over one lap in qualifying thus far this season, but has usually lost out to Mercedes, and often Aston Martin as well, over a race distance.
That pattern was repeated in the Spanish GP, where Carlos Sainz qualified second but was jumped by both Mercedes drivers, as well as the Red Bull of Sergio Perez, in the race.
Vasseur believes that Ferrari will be able to challenge Mercedes in races once it has solved its issues.
"I think as soon as we will unlock the situation with consistency we can imagine to fight with them all over the race," he said.
"With Red Bull it's another story, especially with [Max] Verstappen. He is still much faster than us in quali, much faster in the race."
He insists that Ferrari is keeping up with Mercedes in the development race as both teams strive to catch Red Bull.
"An upgrade when you increase the potential of the car, we are speaking about the top," he said. "You have to think that Mercedes, they are not sleeping.
"Between Miami and today they've also brought a big update in Monaco. It means that they are not sleeping.
"But what we can see on our side is that what we brought this week is paying off in terms of pure performance. And if you take the picture between Miami before the upgrade of Mercedes and today, I think we made a step forward probably in the performance. Mercedes also.
"We are probably a bit faster in quali, but far too inconsistent in the race. If you have a look at Miami, I think first stint of Carlos was good. And the second stint was very poor."
Vasseur indicated that the ongoing strong qualifying form demonstrated that the latest upgrade package had worked well.
"We made a step forward in terms of potential," he said. "The reference in Miami. In quali pace at least we were able to put Carlos on the first row, a step forward probably.
"On the race you could consider that we made a step forward compared to Aston, but it's far from enough.
"We still have a huge delta in terms of performance with Mercedes, quali to race. It's where we have to put all the focus of the company and if we want to come back and to have good races on Sunday so that we are scoring points."
Vasseur conceded that it's hard for Ferrari to judge where the car will be at its most competitive.
"It's really difficult to have a prediction from track to track, where we will be performant or not," he said.
"We are starting now to have a better picture of the car and we know where we perform. I think it's not related to the layout of the track or to the tarmac.
"Miami was completely different at least on the tarmac-wise, and we had exactly the same picture between quali and the race.
"Mercedes is a good reference because they bought a big package in Monaco and the delta is almost the same. I think we made a step forward, but consistency is not there."
