The Philadelphia Eagles were due to visit Washington DC on Tuesday, but the US president rescinded the invitation after several players indicated they would not be attending.
Mr Trump said some of the team’s members “disagree with their president because he insists that they proudly stand for the national anthem, hand on heart, in honour of the great men and women of our military and the people of our country.”
None of the Eagles took a knee during the anthem in 2017.
Philadelphia Mayor Jim Kenney has accused the president of not being “a true patriot”.
He said: “Disinviting them from the White House only proves that our President is not a true patriot, but a fragile egomaniac obsessed with crowd size and afraid of the embarrassment of throwing a party to which no one wants to attend.”
Among the players refusing to attend was Malcolm Jenkins, who said he did not want to be part of a photo opportunity and wanted “to avoid being used as any kind of pawn.”
The Eagles issued a statement, saying: “Watching the entire Eagles community come together has been an inspiration.
“We are truly grateful for all of the support we have received and we are looking forward to continuing our preparations for the 2018 season.”
Wide receiver Torrey Smith, who said previously that he planned to skip the visit, responded to Mr Trump in a series of tweets.
He wrote: “No one refused to go simply because Trump ‘insists’ folks stand for the anthem.
“The president continues to spread the false narrative that players are anti-military.”
The NFL protests began in 2016 when San Francisco 49ers quarterback Colin Kaepernick began silently kneeling on the sidelines while the anthem played.
Kaepernick’s protest was an effort to raise awareness around systemic racism and the killing of black men by police.
Last season, Vice President Mike Pence left a NFL game after about a dozen players took a knee during the anthem.
Mr Trump has repeatedly decried the players’ protest, referring to them as “sons of bitches” who should be fired.
Last month, the NFL announced a new policy requiring players to stand for the anthem if they’re on the field before a game.
:: Meanwhile, four former cheerleaders for the Houston Texans have called on the NFL for fairer pay and work conditions in a letter to the league’s commissioner.
The letter came three days after the cheerleaders sued the Houston Texans in federal court, saying the team had failed to pay them the minimum wage or for overtime and that there was a hostile work environment.
“Cheerleaders are being exploited and mistreated solely because they are women,” said Gloria Allred, the cheerleaders’ attorney.
There was no immediate response from the NFL.
The former cheerleaders’ lawsuit said they were meant to be paid $7.25 (£5.45) an hour for working for the team but were routinely not paid for compulsory work duties.
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This included travelling to and attending events, signing thousands of team calendars, mandatory gym training and compulsory spray tans before every game, the lawsuit said.
The former cheerleaders also allege their coach intimidated them with cruel comments about their appearance and failed to act on their concerns about their safety in interactions with fans.