"I don’t think it’s too much to ask NFL players to respect the Flag and our National Anthem," Pence says.
Explaining why he chose to leave the San Francisco 49ers and Indianapolis Colts game, Pence said in a statement that "President Trump and I will not dignify any event that disrespects our soldiers, our Flag, or our National Anthem".
"While everyone is entitled to their own opinions, I don’t think it’s too much to ask NFL players to respect the Flag and our National Anthem," he said.
Trump later tweeted that he asked Pence to leave on the grounds that the player's actions are "disrespecting our country".
Football players have been taking a knee in silent protest since last year, demonstrating against police brutality and racial injustice. At least one baseball player has joined in the protest.
Prior to the start of Sunday's game, some 49ers chose to kneel while Colts players locked arms during the National Anthem.
The demonstrations are protected free speech under the U.S. Constitution's First Amendment. But Trump has singled them out, repeatedly criticizing athletes over what he claims is a disrespectful action.
49ers safety Eric Reid, who was one of the first to join Colin Kapernick in the demonstrations last year, slammed Pence's action, calling it a "PR stunt".
"This is what systemic oppression looks like," he told reporters after the game. "A man with power comes to the game, tweets a couple things out and leaves the game with an attempt to thwart our efforts."
In a New York Times op-ed, Reid said he and Kapernick chose to kneel rather than sit during the National Anthem "because it’s a respectful gesture".
"It baffles me that our protest is still being misconstrued as disrespectful to the country, flag and military personnel. We chose it because it’s exactly the opposite," he wrote.
The National Anthem is played before every football game, as well as most sporting events.