The incident occurred with 29.2 seconds remaining in the fourth quarter of the Lakers' 105-95 loss to the Los Angeles Clippers on Friday at Staples Center.
Blake had eight points and two assists against the Clippers in his first start for the injured Steve Nash, but shot just 2-of-6 from the field.
Blake and the fan initially exchanged words after the fan told Blake, "You need to knock down those open shots," and Blake snapped back with a comment, ESPNLosAngeles.com has learned. Later, Blake again made comments to the fan shortly after fouling out of the game.
"It's an unfortunate misunderstanding and a heat-of-the-moment type of thing," Blake said after practice Tuesday. "It's one of those things I'm not proud of, the way I handled it, and I look forward to growing as a person and moving forward from it."
Blake met with the fan, Lance Jackson, and his father, Steve Jackson, at the Lakers' practice facility Tuesday. The Jacksons are longtime courtside season-ticket holders and have a strong relationship with the team.
Many Lakers players have worked out at the Jacksons' private gym at their home, and some visiting NBA teams have actually conducted practice at the Jackson residence.
"We got a chance to speak and talk about the situation, and I just let them know I was sorry for the way I acted," Blake said. "I didn't handle myself the way I want to, and we were able to talk and hopefully can build a relationship off of that."
Blake said the circumstances surrounding the Lakers' poor start caused his frustrations to boil over.
"It was an emotional game for me, losing a third game in a row and this and that, but there are no excuses," Blake said. "It was just a spur-of-the-moment bad decision."
The 10-year veteran said he had never had an encounter with a fan such as that in the past.
"I'm feisty and can get into it on the court, but I've never taken it anywhere else," Blake said. "That's what I want to be known for, and they're great people and they didn't deserve to have that type of interaction with a player."