Vowles told reporters at the Dutch Grand Prix that the extensions, announced this week, were "incredibly important" as a public vote of confidence in a team whose performance on the track has plunged after the former champions finished fifth last season.
Williams are ninth of 11 teams with 11 points - six scored by Sainz and five by Albon.
"I was concerned about losing both because they are world championship material drivers that deserve the opportunity to be fighting for podiums or more and we haven't delivered that," Vowles told reporters at the Dutch Grand Prix on Friday.
"What I'm thankful for is the moment we have problems, they stood by our side. It shows the outside world... that they believe in what the future looks like.
"Probably the best way to summarise it to you is the factory (employees) - there was a weight lifted off it this week as a result of it (the announcements) and I've seen them move forward at a much faster pace as a result, so the belief is real and tangible."
Sainz in for the long haul
Sainz, a four-time race winner with Ferrari, had been linked in media speculation with Audi before agreeing a multi-year extension. He told reporters on Thursday that he had taken his time to assess the situation but was not the kind of person to jump ship as soon as the going got tough.
"I think in the back of my head I wanted to always renew but I was worried, concerned that we need to make sure this (situation) doesn't happen again," he said, explaining his thinking as: "I want to be here in the long term, how can I get out of this with this team, how can we get out of this together as soon as possible."
Albon, who has now started 100 races with Williams, had less clear alternatives and has signed a one-year extension.
Vowles said Williams had convinced Sainz that the team had turned a corner and, although still way off where they wanted to be, were back on the right path.
He said simulation technology that had not been available at the start of 2025 only came online last November when the 2026 car was already almost done.
"What we were doing was using educated guessing, and we got some of it wrong," said the boss. "We developed at the wrong rear ride height, as did Aston (Martin) for that matter... that doesn't seem like a huge amount, but you're aerodynamically developing in completely wrong space."
The Williams car was late to testing, overweight and lacking downforce. The car brought to Miami in May, round four of the championship, was effectively the one intended for the March opener in Melbourne.
Vowles said Williams would not be 'fixed' in 12 months, with the cost cap limiting what could be done and 20 years of under-investment to make up.
"What I'm doing right now is putting a lot of cost cap dollars into fixing problems that other teams don't have," he added, saying decisions were being taken for the next five years.
Former McLaren chief operating officer Piers Thynne joined this month with a focus on streamlining production processes, planning and modernising facilities. Vowles said he was a huge asset, who understood what championship level looked like.
Williams, dominant in the 1980s and 1990s, last won a championship in 1997.