Scott said he does not support gay marriage on moral grounds but does not defile gay people.
"Gays have been here when I was born and they're going to be here after I'm gone," he said.
Supporters of Carson — one of two Muslims in Congress — have previously criticized Scott and his supporters for sending anti-Muslim messages. Scott's website says he would fight Muslim extremism and that Islam "advocates the eventual elimination of all Christians and Jews."
Carson campaign manager Matt Hammond said Carson has been and will remain a champion for civil rights.
"Once again, the Scott campaign has gone out of its way to insult the people of Indianapolis through thoughtless and prejudiced speech," Hammond said. "Although his campaign manager has resigned, we are far from confident that this will raise the level of respect and thoughtful dialogue coming from his campaign."
Scott was the Republican challenger to Sen. Evan Bayh in 2004 and has lost previous congressional campaigns. He defeated Carlos May, a former aide to Indianapolis Mayor Greg Ballard who had been endorsed by the Marion County Republican Party, in the May primary.
Carson had $381,000 on hand through June 30, according to federal campaign finance reports, while Scott had just $1,800 on hand.
Carson is seeking his second full term to the seat once held by his late grandmother, Julia Carson. The district covers most of Indianapolis and is heavily Democratic.