Dest, 21, was struggling with fitness issues when Xavi was appointed in November and subsequently spent the best part of two months either injured, playing out of position or on the bench.
"Everyone is improving," Xavi said in a news conference after Sunday's impressive 4-1 win at Valencia which saw Barca return to the top four in LaLiga.
"Let's take Sergino as an example. When we got here, he wasn't doing so well, but now he is doing great. I thought he was spectacularly good [against Valencia], both with the ball and without it. I am really happy with his progress."
Dest has bounced back from being left out of the squad entirely for the Spanish Supercopa defeat to Real Madrid at the start of January by starting three of the last four games in LaLiga.
With Dani Alves serving a two-match ban, he has played 90 minutes in the last two games away at local rivals Espanyol and Valencia, while he came off the bench in last Thursday's 1-1 draw with Napoli in the Europa League.
"I feel good on a personal level, Xavi gave me the trust now to play again," Dest told ESPN after the Valencia win.
"If I don't play, I always train harder to get into the team again, so I will never stop. So, if I don't play, I train really hard to get my stamina back and everything and get stronger. And when I can play, I try to show that I want to be there.
"I feel great. Three points away is always a good feeling and, as a team, we fought really hard. I think the intensity was the key, we helped each other a lot. The teamwork was good."
The player's camp always maintained that Xavi was yet to see the best of the United States defender, according to ESPN sources. Dest has suffered from several injuries this season and, at the request of the club, played while not fully fit in November and December in an unfamiliar attacking role to help the team, which set back his recovery.
He later tested positive for COVID-19, setting him back further, but has been fully fit since the end of January and will now compete with Alves for a starting berth between now and the end of the season.
However, with Alves not registered for the Europa League, Dest is likely to be Barca's first-choice right-back in Europe if they get past Napoli on Thursday as he fights to remain part of Xavi's long-term plans.
Dest, who joined Barca from Ajax for €20 million in 2020, has made 22 appearances in all competitions this season having played 41 times in his debut season at Camp Nou.