Mr Goodell said he would be contacting players who had voiced concerns about the league.
"Protests around the country are emblematic of the centuries of silence, inequality and oppression of black players, coaches, fans and staff," Mr Goodell said. "I will be reaching out to players who have raised their voices and others on how we can improve."
The NFL sent the video out just hours after President Donald Trump renewed his call for an end to kneeling protests during the national anthem.
"We should be standing up straight and tall, ideally with a salute, or a hand on heart," Mr Trump wrote on Twitter. "There are other things you can protest, but not our Great American Flag - NO KNEELING!"
The statement was a response to quarterback Drew Brees, who apologised this week for equating the kneeling protest with disrespecting the American flag.
On Thursday, several players, including reigning Super Bowl MVP Patrick Mahomes of the Kansas City Chiefs, appeared in a video on social media calling for the league to "admit wrong in silencing" players and to support protests.
"How many times do we need to ask you to listen to your players?" Chiefs player Tyrann Mathieu said in the video.
The league also faced criticism earlier this year when just one of five head-coaching vacancies went to a non-white candidate in the most recent hiring cycle, and last month the NFL introduced rules designed to boost racial diversity among coaching staffs.
The chief of American football's top league has admitted that it was wrong for not letting players peacefully protest over police brutality against black people.
Roger Goodell, the commissioner of the National Football League (NFL), said his organisation made mistakes in a video on Friday which denounced racism in the United States following widespread protests over the death of George Floyd.
"We, the National Football League, admit we were wrong for not listening to NFL players earlier and encourage all to speak out and peacefully protest," Mr Goodell said. "We, the National Football League, believe black lives matter."
The NFL has been locked in an debate with players over kneeling protests during the customary pre-game rendition of the national anthem. The practice was popularised by quarterback Colin Kaepernick in 2016 to protest racial injustice and police brutality.
Kaepernick, who has not played in the NFL since 2017, filed a grievance against the league later that year, claiming that teams colluded not to sign him after he left the San Francisco 49ers. The NFL and Kaepernick settled in 2019.