“Football has always evolved, and it always will,” he told an overflow crowd of a few hundred. “Make no mistake: change does not inhibit the game; it improves it.”

In a long-planned appearance that came four days after three starting NFL quarterbacks were knocked out with concussions, Goodell said that the league has already improved the way it handles hits to the head.

San Francisco’s Alex Smith, Chicago’s Jay Cutler and Philadelphia’s Michael Vick were all diagnosed with concussions in Sunday’s games. Goodell said that all three were taken out “as soon as they showed symptoms,” a claim that was challenged by a member of the audience during the period for questions who noted that Smith and Cutler kept playing for a short time after being injured.

“It was identified and they were taken out of the game,” the commissioner said. “Even a few years ago, I’m not sure you would have seen that.”

Listing some of the safety measures that have been incorporated into the sport both before and since he became commissioner, Goodell mentioned the elimination of the flying wedge that was first employed by Harvard in the 1800s and the change in kickoffs last season that he credited for a 40 percent reduction in concussions on returns. He said the league is looking into better helmets and sponsoring scientific research that could make the game still safer.

“Not long ago, the game allowed the head slap, tackling by the face mask, horse-collar tackles, dangerous blocks, and hits to the head of defenseless receivers and quarterbacks. All of that has changed,” he said.

“My commitment has been and will continue to be to change the culture of football to better protect players without changing the essence of what makes the game so popular. It has been done.

“And it will be done.”

Football has never been so popular — and its popularity is still rising, Goodell said. The 16 most-watched TV shows this fall — other than the presidential debates — were NFL games; the second-most popular sport to professional football is college football, Goodell said, quoting President Barack Obama as saying, “You don’t go anyplace where folks don’t talk about football.”

But the sport’s popularity has also been jeopardized by an onslaught of reports linking it to the brain damage that can lead to memory loss, depression and suicide among retired players.

“We are well aware of social commentators who now question our future. And I am here to tell you: If we are at another crossroads, we have already taken the right path,” Goodell said. “We took it a long time ago, and our commitment to stay on it will not waver.”

Calling it the sport’s biggest challenge, Goodell said his goal is to change the sport’s culture — a culture in which players and coaches are discouraged from hiding injuries to keep players on the field. The problem is not unique to football, he said, noting that athletes in other sports are hesitant to leave when others are still competing or, in the case of the military, in danger.

“The culture of the athlete is still too much of a play-through-it, rather than player safety mentality. Many players have publicly admitted to hiding concussions and other head injuries,” he said, telling the story of a family friend with a 15-year-old daughter who hid a concussion because she didn’t want to come out of a field hockey game.

“It’s the warrior mentality — in a 15-year-old girl. This is unfortunate, but we are working with players, team doctors and coaches to change that culture. It is changing, but will take more time, resolve, patience, and determination.”

Goodell said that his twin daughters play middle school lacrosse and soccer.

“I am concerned for their safety,” he said. “I want them to play, but I want them to play for coaches who know how to teach proper techniques and who are trained in the safety of their sport.”

Research has shown that repeated hits to the head, even those that do not cause concussions, can cause brain damage in players in contact sports, including football, hockey and boxing. Dr. Robert Stern, one of the researchers who has been looking into brain damage caused by concussions, said the steps the league has taken are “making a huge difference.”

But the changes are coming too late for thousands of former players who claim the NFL withheld information on the damage concussions can do to their long-term health. More than 3,500 former players — including at least 26 members of the Pro Football Hall of Fame — have sued the NFL, saying not enough was done to inform them about the dangers of concussions, and not enough is being done today to take care of them.

Asked about former players, Goodell said, “It’s no secret that we have challenges in that area.” But he noted that the league has worked with former players on other medical problems: paying for joint replacements if they can’t afford them and warning of the dangers of cardiovascular disease if they stop working out once they stop playing.

“We want players to enjoy long and prosperous careers and healthy lives off the field,” Goodell said. “So we focus relentlessly on player health and safety, while also keeping the game fun and unpredictable.”

Goodell also claimed that it is only more recently that the danger of repeated concussions has been understood. Leadership, he said, “means facing up to your challenges and working tirelessly to make sure you make the right choices, for the right reasons, based on science and facts, not speculation.”

Another audience member asked Goodell if the four-game preseason, with talk of an 18-game regular-season schedule, undermined his claims of concern for player safety. Goodell said the league had an option in the former collective bargaining agreement to go to a 20-game schedule, but chose not to.

The exhibition season may be shortened, he said — but not because of player safety.

“It just does not meet the standard of quality that the NFL is all about,” he said.