A group of retired NFL players who opposed the $1 billion concussion settlement between the league and thousands of former players will not appeal the case to the Supreme Court, with former All-Pro offensive lineman Alan Faneca calling the decision "for the greater good of everybody."

"It's been a long road, and I guess there comes a point in time when you see the end of the road," Faneca, one of the players who challenged the deal, told the New York Post.

A federal appeals court upheld the settlement in April, and the deadline for filing an appeal to the Supreme Court was Monday.

Former players already diagnosed with brain injuries linked to repeated concussions can begin receiving benefits within three months, Tom Girardi, who represented the players in the settlement, told the Post. He estimates that between 1,000 and 1,500 players would be eligible for payments now.

Players could receive up to $5 million individually if they were diagnosed with amyotrophic lateral sclerosis (ALS), also known as Lou Gehrig's disease. The next-highest award is $4 million for families of a player with a post-mortem finding of chronic traumatic encephalopathy, or CTE, and $3.5 million for players with Parkinson's or Alzheimer's.

"I think the settlement provides a small window for a large group of guys," Faneca told the Post.

The settlement covers more than 20,000 NFL retirees for the next 65 years. The league estimates that 6,000 former players, or nearly three in 10, could develop Alzheimer's disease or moderate dementia.

Fewer than 200 of those retirees opted out of the settlement, while 99 percent approved.

As part of the settlement, the NFL admitted no fault. A league official speaking to Congress in March acknowledged for the first time a definite link between football and CTE. But the appeals court said that admission was not grounds to overturn the settlement.

The league has been dogged for years by complaints that it hid the risks of repeated concussions in order to return players to the field. The deal avoids the need for a trial and means the NFL might never have to disclose what it knew, and when, about the risks and treatment of repeated concussions.

Some players who challenged the deal argued that it does not cover mood and behavioral disorders that some researchers link to CTE.

Information from The Associated Press was used in this report.