Over the Monaco weekend, Ferrari and McLaren headlined the order as championship leaders Red Bull struggled to contend with the street circuit's bumps and could only manage sixth through Max Verstappen - sandwiched by the two Mercedes drivers.
Vasseur acknowledged that the field had compressed in 2024 and that the three teams who had won races so far this season could all contend for further victories depending on the layout of each upcoming circuit.
The Frenchman was keen to add that it was important for Ferrari to maintain its progress, and that knowing Red Bull was beatable did not change the team's motivation to challenge for honours in F1. He stated that it would be the "worst-case scenario" for Ferrari to believe that its job was already done.
"It's not a matter of motivation because the motivation is there for a while, but it's self-confidence for the drivers, for the team," Vasseur explained.
"And for sure, as soon as you are in a position to win you pay more attention to details, you have a kind of snowball effect. This is part of the improvement of the last six or seven months.
"We have to continue like this, but the worst-case scenario would be to imagine that it's done, that it will be like this until the end.
"Because I'm convinced that first, as I said before, we'll have different tracks with different layouts, different characteristics. We are competing more with McLaren or Red Bull and it will be up and down until the end of the season.
"We have to score good points when we are not at the top and to be able to win when we are there. But nothing changes."
Vasseur added that Red Bull will continue to have the advantage at future circuits on the calendar and that, even in races where Ferrari might not be on top, the team will need to be "opportunistic" to secure a healthy points haul from them.
He felt that, should Ferrari and McLaren continue to make progress, they will provide "tight" competition for Red Bull over the rest of the season.
"I think now we have at least three teams – but I think Mercedes is not that far away – at least three teams able to fight for the pole position, able to fight for the win. It's exciting and it will be, I hope, like this until the end of the season.
"For sure, depending from track to track, we'll have perhaps Red Bull with an advantage, or Ferrari, or McLaren. And we'll have to be opportunistic.
"It was not always the case in the past; last year, we lost far too many points into the season, and this season we made a huge step forward on this one also.
"We are much more opportunistic, and it will be like this until the end of the season, that the fight will be tight."
Additional reporting by Jonathan Noble and Stuart Codling
