World number 48 Norrie netted a shot while trailing 6-2, 5-3 to Diaz Acosta and threw his racket in frustration, before going over to the fan sitting in the front row, who appeared unhurt.
The Brit was issued a warning by the chair umpire for unsportsmanlike conduct.
"I wasn't meaning to do that but it's still not ideal to be doing that and I've never done something like that," said Norrie, who represented New Zealand as a junior and previously lived in Auckland.
"(The spectator) was laughing and I just said 'so sorry, I didn't mean to do that.' And she said 'yeah, I'm completely OK.' That was not a big deal. But as we saw with some other players, you can easily be defaulted if it catches them in the wrong spot or they're not looking or something.
"I was not meaning to do that and it is completely not me to do something like that. I apologised very quickly and I want to apologise in general. I'm not happy with how I behaved."
At the 2020 US Open, 24-time Grand Slam champion Novak Djokovic was defaulted in the fourth round after accidentally hitting a line judge in the throat with a ball.