Sargeant's future at Williams has been in doubt in the wake of a run of accidents since the summer break.
He crashed heavily in qualifying and the race at the Dutch Grand Prix, hit the barriers at the Singapore GP, and then went off in a big accident during Q1 for the Japanese GP last weekend.
Those run of incidents come at a time when Williams wants to see the American show steady improvement over the remainder of the campaign to show that he can step it up alongside Alex Albon next season.
While Sargeant's latest crash prompted early speculation that Felipe Drugovich, Liam Lawson or Mick Schumacher could be in the frame to replace Sargeant, Vowles has poured cold water on any talk that he is definitely looking elsewhere for his team's second seat.
Instead, speaking on his post-race 'Vowles Verdict' video on the Williams website, he declared that the team wanted Sargeant to succeed – and that it had to work with him to make it happen.
"Logan has very clear targets that he has to hit before the end of the season and we're working with him continuously," said Vowles.
"That's the important point: we're working with him. We want him to succeed, and we want him in the car next year. This is very much on us as well.
"We have taken someone straight from Formula 2 without any significant testing, put a day and a half in Bahrain in this car, and then wished them well on a season that has been awfully challenging for rookie drivers, full stop."
While Sargeant's Suzuka qualifying crash grabbed the attention last week, Vowles said that digging deeper into the data at the Japanese Grand Prix had actually shown the very progress that Williams wanted to see.
"There were some very positive signs to take out of it," he said. "First and foremost, Logan is not on the same aerodynamic specification as Alex was.
"We have updates that are on Alex's car that are not on Logan's due to the amount of attrition we've had this year. So often when you see a performance offset, it's not quite what it would seem on the timing pages.
"Furthermore, to that, if we look at the case of Suzuka, he did a build-up across the weekend. As he went into FP3. he did a time that matched Alex and, as we go into qualifying until the accident, he was overlaying line online within a 10th of Alex's performance as well, at one of the trickiest circuits of the season.
"So, the progress is there in certain forms, but very clearly being marred by a number of other issues and accidents that have appeared as well."
Vowles made clear that having brought Sargeant on, Williams was willing to invest more in him, and was far from giving up.
"We will continue to work with Logan and invest in Logan, as we want him to succeed," he said. "He's on a journey with us as Williams.
"We have a young driver programme that we will continue to invest in. Only at the point where all of us come to the conclusion that we've reached the end of that road will we make any decisions. But we're nowhere near that yet."
