After finishing seventh in 2022, Aston Martin has made a major leap forward, holding second in the constructors' standings after three races by virtue of Fernando Alonso's three consecutive podiums.
It is the most significant year-on-year improvement for an F1 team in years, but Stroll's ambitions reach much further.
The Canadian billionaire has been assembling a team to fight for world titles within the next few years by headhunting top talent from rival teams, including former Red Bull aero chief Dan Fallows.
The team's major rebuild is illustrated by the construction of a new state-of-the-art £200 million Silverstone headquarters, the first stage of which is due to open next month.
And even as he appreciated the team's 2023 improvement, Krack revealed that Stroll has wasted no time demanding even more.
"It's quite easy. Lawrence's mission statement is pretty clear. He has not been having any delay in telling us: 'When are we going to win the next one?'," Krack replied when asked by Motorsport.com how Stroll reacted to the team's success.
"Obviously he's happy that we have made a step, but this is not enough for his ambitions.
"The good thing with Lawrence is you know where you stand. He wants more and we will have to deliver more."
Aston Martin's resurgence started during the 2022 season, when it had already made great strides after a disappointing start.
When asked if the team can keep up a similar development pace this season, Krack said: "We have managed last year to develop the car substantially. We started from a higher baseline this year, so it will not be as easy as it was last year.
"But we have to make progress if we want to stay where we are, because even if we do nothing we will go backwards.
"I am quite confident that we can bring performance upgrades to the car but because it is all related. We will only in time if it is efficient or not.
"I think we know roughly what we have to do and this is what has already started."