The 21-year-old secured the biggest win of his career, and his first over a top-10 player.
"I really don't know even what to say right now," Anderson said.
"I really tried to give myself the best shot walking in today. I kept telling myself I can do this. I've just got to believe in myself, play my game.
"But even still, just knowing what he's done and what a great player he is, and to have actually beaten him, it's a tremendous experience for me."
|"He was winning too easy in the first set his service games, and I wasn't aggressive enough."|
The South African newcomer reached the final of the ATP event in Las Vegas earlier in March, but had lost the only two ATP matches he had ever played before that tournament.
Djokovic, one of the 32 seeded players who received a first-round bye, was launching his title defence fresh from claiming the first Masters Series title of 2008 at Indian Wells on Sunday.
Other seeds out
"It was our first meeting, and I never saw him playing before," Djokovic said.
"He surprised me with the way he was serving. I wasn't moving on my returns good enough, and obviously that resulted in easy service games.
"He was winning too easy in the first set his service games, and I wasn't aggressive enough. Then when I needed to use my chances in the third set, I made some unforced errors, which were really crucial.
"I was maybe going for too much," the Serb added.
"Obviously, he's really tall, and with that height, you expect him not to move so well. But he has a good coordination. He has a good feel for the ball. He's a good player."
In other second-round men's matches on Friday, second-seeded Spaniard Rafael Nadal eased into the third round with a 7-5, 6-2 victory over German qualifier Benjamin Becker.
Nadal, who lost to Djokovic in the semi-finals at Indian Wells, is seeking his first title of 2008.
A further two top-eight seeds fell along with Djokovic, as Russian Dmitry Tursunov outlasted number eight Richard Gasquet of France 6-3, 6-7, 7-6 and Belgian Xavier Malisse made easy work of seventh-seeded David Nalbandian of Argentina 6-1, 6-4.