The eight opt-outs for the Patriots are the most in the NFL. LaCosse's decision leaves the Patriots with five tight ends on their roster: third-year player Ryan Izzo, rookie draft picks Devin Asiasi and Dalton Keene, and undrafted rookies Jake Burt and Rashod Berry.
In his first season with the Patriots last year, LaCosse had 13 catches for 131 yards and a touchdown in 11 games.
LaCosse joins Patrick Chung, Dont'a Hightower, Marcus Cannon, Brandon Bolden, Danny Vitale, Najee Toran and Marqise Lee as Patriots who have chosen to opt out.
Speaking to the media on Friday, Belichick said he respected the decisions of the six players who had opted out to that point and supported them "100 percent." Lee became the seventh player to opt out on Saturday.
"Well, I respect all of them. I respect all of the players on our team," Belichick said. "We all have to make decisions and I talked to those guys and they explained their situations. They had to make the decision that was best for them and I totally respect and support it 100 percent.
"I think everybody has to make their own individual decisions on that," he added. "They have to weigh their own situation. Each one of us is unique and we all have different lives, situations, families, environments, and so forth and so on. There’s no two situations that are the same. Everybody will have to make their own decision on that."