NFL star Adrian Peterson is currently facing child abuse charges in Texas. (Jeff Curry/USA TODAY Sports)

Former NFL players told Commissioner Roger Goodell during a meeting Tuesday in New York that when the league revamps its personal conduct policy, the sport’s leaders must be willing to permanently ban those players who fail miserably to adhere to the newly articulated standards, even if they are stars.

“Mike Singletary and Marty Lyons talked about, ‘The NFL represents excellence,’ ” Troy Vincent, the NFL’s executive vice president of football operations, said in a telephone interview late Tuesday. “Mike Singletary and Marty Lyons drilled that home: ‘We’ve lost sight of what NFL excellence means.’

“Singletary looked right across the table at the commissioner and said: ‘Don’t compromise our excellence. We can’t waste our time on a few individuals when there are long lines of people who want to come in and do it right.’ We talked about cultural issues. We talked about trust. The theme really was, ‘You can’t save everybody.’ There was one consensus: ‘You have to be willing to depart with some of our stars,’ ” said Vincent, who participated in the meeting.

Goodell and Vincent met for about 3-1/2 hours Tuesday with a group of 11 former players. Vincent called it the beginning of a dialogue that will include current players, NFL Players Association leaders, others within the sport and outside experts on domestic violence and other issues. The participation of players, both current and former, will be pivotal, in Vincent’s view, as those within the game try to balance players’ rights with the the pressures placed on the league and teams to act immediately in some disciplinary cases rather than waiting for the legal process to play out.

“None of this works without player input, player buy-in,” Vincent said. “These are non-collective bargaining issues. After last week and the things we went through, we don’t have time to wait. We’ve got to get thoughts from as many people as possible. And to me, that starts with current and former players. Lyons, [Tony] Paige and Singletary, they set the stage today.”

Goodell said Friday he would modify the conduct policy. The announcement came with Goodell, the league and some teams facing withering criticism for their handling of the recent legal issues of players Ray Rice, Adrian Peterson and Greg Hardy. All three are standout players and Peterson is among the league’s most celebrated stars.

“We were asked: What are we trying to do on the front end [to prevent players from getting into trouble]?” Vincent said. “We were asked: How do we hold clubs more accountable? People said, ‘We can’t leave it up to the coach. Then we have 32 different standards. We need to have one standard.’ ”

Vincent has had many roles in the sport from player to union president to league executive. He and others who were in the room Tuesday participated in similar discussions when Goodell, with the cooperation of late union chief Gene Upshaw, toughened the sport’s personal conduct penalties in 2007, targeting repeat offenders. Goodell said Friday that the conduct policy has become outdated and was insufficient to deal with the recent issues faced by the sport in the Rice, Peterson and Hardy cases.

The relationship between the league and union has been more combative in recent years with DeMaurice Smith as the NFLPA’s executive director. But Vincent said he believes everyone in the sport will see the need to work together now on these issues.

“We’re not talking about collective bargaining,” Vincent said. “We’re talking about the game and the integrity of the game. I’ve been in collective bargaining talks and this is not that. [Former Vikings and Ravens center] Matt Birk said it, too. We can disagree on a lot of things. We can disagree on who gets what share [of revenues]. But this is the game. This affects our households. This is our livelihoods and our passion. This is too important. I’m confident that De Smith and the union will see it that way because this is too important.”

The former players stressed to Goodell during Tuesday’s meeting that the reworked conduct policy resulting from these conversations must be straightforward.

“Mike [Singletary] and Robert Porcher said, ‘Let’s move away from the legal talk. Remove the gray area. Make it clear and make it plain. There is no negotiation,’ ” Vincent said. “It was, ‘Hey, these are the standards. When they’re written out, make it clear and not vague.’ ”

The players who participated in Tuesday’s meeting included Singletary, Porcher, Lyons, Paige, Birk, Willie McGinest, Roman Oben, Eddie Mason, Patrick Kerney, Charles Way and Scott Turner. Other former players such as Curtis Martin and Ray Lewis are eager to participate in the process but were unable to attend Tuesday, according to Vincent.

“Based on where we are, it’s personal,” Vincent said. “It’s got to mean that much to you. Most people don’t remember it was player input the last time we did this. It’s how we got here. For this to work, there has to be player input.”