Alves returned to Barcelona in November 2021 after his contract with Sao Paulo expired, and the defender featured on 15 occasions for the club in the second half of the 2021-22 campaign.
The Catalan outfit decided against renewing his deal, though, and he therefore departed on a free transfer.
The 39-year-old has praised Barcelona boss Xavi and president Joan Laporta for allowing him to return to the club for a second spell, having previously represented the team between 2008 and 2016.
However, the Brazilian has hit out at Blaugrana's off-the-field conduct, claiming that they 'do not care about the people who made history at the club'.
"I was happy to be back in Barcelona. I dreamed for five years of living that second stage," Alves told The Guardian. "The only thing I didn't like was how my farewell was handled.
"Since I arrived I made it very clear that I was no longer a 20-year-old and that I wanted things to be done straight, without hiding things. But this club has sinned in recent years. Barcelona doesn't care about the people who made history at the club. As a Cule [Barcelona fan] I would like Barcelona to do things differently.
"I am eternally grateful to Xavi and the president for bringing me back.I found a club full of young people with incredible ideas on the pitch.
"The club needs to improve the work off the pitch. The mentality is totally the opposite of what we built a few years ago. Everything that happens on the pitch is a reflection of what happens off it."
Alves has won 125 caps for Brazil, captaining his national side against South Korea and Japan in their June friendlies, and he is bidding to make their squad for the 2022 World Cup, with a decision on his next club expected to be made in the near future.
"I like challenges and I adapt to any situation," Alves said when questioned on his future. "Interesting things have come up, I'm studying them."
Athletico Paranaense, Fluminense, and Pumas are among the clubs believed to be attempting to sign the experienced defender this summer.
Alves played an valuable role for Barcelona in the second half of last season, featuring on 15 occasions, including 13 times in La Liga, contributing one goal and three assists.
"I would like to thank all the staff for the opportunity they gave me to return to this club and to be able to wear that wonderful shirt again. You don't know how happy I am," the defender said when confirming his exit.
Across two spells, Alves made 406 appearances for Barcelona, contributing 22 goals and 104 assists in the process, winning six La Liga titles, four Copa del Rey crowns and three Champions League titles.