The embattled kicker admitted to years of abusive behavior toward his ex-wife in newly released police documents.
CBS Sports' Jason La Canfora reported Friday that some teams are unhappy with how the situation has been handled by the league.
There have been parallels drawn between the NFL's handling of the Brown case and the Ray Rice domestic violence scandal at the end of the 2013 season.
San Francisco 49ers wide receiver Torrey Smith joined the chorus of criticism with a series of tweets in response to the news that Brown was placed on the commissioner's exempt list, which still allows him to get paid while he is not eligible to play.
In addition, NFL owners, executives, coaches and players have privately expressed their displeasure over how the league and the Giants have handled the domestic violence allegations against Brown, sources confirmed to ESPN.
One team owner called the situation an "embarrassment," according to ESPN.
The NFL on Friday placed Brown on the commissioner's exempt list -- a move that only NFL commission Roger Goodell has the authority to make -- after documents released by the King County (Wash.) Sheriff's Office showed the kicker acknowledged physical, verbal and emotional abuse against his then-wife Molly Brown.
The kicker did not travel with the team for Sunday's game in London against the Los Angeles Rams. Sources told ESPN's Chris Mortensen that the 37-year-old veteran is done with the Giants.
The NFL suspended the kicker for only one game for the May 2015 incident -- Brown was arrested for allegedly grabbing the wrist of his then-wife in a heated dispute at a home the couple shared in Woodinville, Wash. -- because of "insufficient information to corroborate prior allegations."
The Giants then signed Brown to a two-year, $4 million extension this offseason. By being placed on the commissioner's exempt list, Brown will still be able to collect his base salary of approximately $1.15 million.
In a letter sent to Brown on Friday, NFL senior vice president Adolpho Birch said the league wants to investigate further upon learning of the new documents.
Goodell's trip to London for Sunday's game brought questions about the Brown case.
In an interview with the BBC, Goodell said the NFL "asked repeatedly" for the documents before they were made public by the King County Sheriff's Department.
The commissioner said the initial decision to suspend Brown for one game at the start of the season was based on the facts they had at the time.
"We take this issue incredibly seriously," Goodell told the BBC. "This is something we've been working on with policy changes, to educating our players to make sure they understand how they deal with issues with their family, give them resources to be able to deal with this.
"But when it happens, we're not going to tolerate it. So we have some new information here, we'll evaluate that in the context of our policy, and we'll take it from there."
Goodell was asked if he is disappointed in the Giants and an investigative process that didn't uncover more details.
"That's why we'd like to speak to the people involved, whether it's the victim or the people involved that may have information, including law enforcement," Goodell said.
"But we understand that in certain cases, they may not be permitted to talk to us or want to talk to us, and we don't make judgments on people where they do that. What we want to do is get the facts, and when we get the facts, we're going to aggressively pursue that, and we'll apply our policy."
Two league officials told ESPN off the record that they believe the NFL was disinterested in the Brown case when compared to the league's high-profile Deflategate case involving quarterback Tom Brady of the New England Patriots.
"It's exciting to be here," Gould said soon after arriving in London. "Obviously, it's a great opportunity to play for one of the most heralded franchises in the NFL. Happy to get the opportunity and thankful to get the opportunity. Looking forward to having some fun."
"I've seen him make a lot of kicks against me in the past," McAdoo said. "He's been successful. We're hoping that continues."