"My response is I don't see it as disrespect at all,'' Kapler said.
"I see nothing more American than standing up for what you believe in. I see nothing more patriotic than peaceful protests when things are frustrating and upsetting," Kapler said.
Kapler knelt alongside multiple Giants players during the anthem in Monday's game against the Oakland Athletics.
The Giants' posted a video of its team members kneeling on the team's official Twitter account with the caption "#BlackLivesMatter."
Trump, a frequent critic of anthem protests, responded in a tweet.
"Looking forward to live sports, but any time I witness a player kneeling during the National Anthem, a sign of great disrespect for our Country and our Flag, the game is over for me!" Trump wrote.
Kapler, who took a knee with players again on Tuesday, said Trump's criticism will not dissuade him.
"There's nobody that should make us stop doing the right thing. It doesn't matter what leader says that they're not going to be following a game. What matters the most is that we're unwavering in trying to do what's right," he said. "What guides our decision is standing up for people who need us to stand up for them.''
Kapler was raised in an atmosphere of activism and has been outspoken about the Black Lives Matter movement, according to the Giants website.
Athletes have been kneeling for the anthem to support protests for social justice and racial equality, as the country comes to terms with systemic racism and protests have erupted over the killings of Black people at the hands of police.
Anthem demonstrations were popularized by former San Francisco 49ers quarterback Colin Kaepernick, who first sat and then kneeled for the anthem in 2016.
In an interview after Monday's game, Kapler said that the Giants had conversations about what to do during the anthem for three days leading up to the exhibition.
"I told them that I wanted to amplify their voices, and I wanted to amplify the voice of the Black community and marginalized communities as well," he said. "I told them that I wanted to use my platform to demonstrate my dissatisfaction with the way we've handled racism in our country. I wanted to demonstrate my dissatisfaction with our clear, systemic racism in our country, and I wanted them to know that they got to make their own decisions and we would respect and support those decisions."
Farhan Zaidi, Giants president of baseball operations, said in a statement the team was proud of players and staff for participating in the national discussion on racial injustice.
"We support those who knelt to peacefully protest racial injustice and those who stood to express love of country. We do not see these as mutually exclusive sentiments and believe freedom to express both is what our country is about," Zaidi said.
