The All Whites refused to emerge for the second half after Boxall and his team-mates claimed Qatar winger Yousuf Abdurisag made a "significant racist slur" five minutes before the interval.
New Zealand's players did not return for the second half after reporting the incident to officials.
"It's one of those things, I'm pretty competitive and I say a lot of things that I wouldn't want my kids to hear, but that's certainly crossing the line," Boxall, who is of Samoan heritage and plays for MLS side Minnesota United, told the Star Tribune.
"It's not something I'd ever say. I didn't really take great offence to it, but I think it's one of those things you can't allow on a football field.
"I'm sure it's a slur he uses colloquially every day, but when it's directed at another player on the field, you can't get away with that.
"It's not something I take personally. I'm proud of my team-mates for taking the stand they did."
New Zealand Football said after the incident that they intended to raise the matter with FIFA, the game's governing body.
The Qatar Football Association denied Abdurisag used discriminatory language during an exchange of words "in the heat of the moment" where he was the victim of racial slurs.
"I've moved on and I'm ready to get back to work," Boxall said of the incident.
"We've taken that stand, and now it's out of our control and just let the powers that be sort everything out now."
