Williams had skipped the showpiece event at the desert resort after winning her second title here by beating Kim Clijsters in a final marred by the behaviour of some spectators who booed and heckled the American and her family.
The reaction was in apparent response to Serena's sister Venus having withdrawn from their semi-final that year just minutes before the match.
"The whole point of me coming back was not to necessarily focus on what happened 14 years ago," world number one Williams, 33, told a packed news conference at the Indian Wells Tennis Garden.
"It was more or less to focus on how I felt, if it was the right opportunity for me to come back now and for me to be at this tournament. I just felt like it was time.
"There's not one thing that says I should come back, that I should come back in 2015. I just felt like it was the right time for me to come back here and try to do the best that I could."
Spectators vented their displeasure with the withdrawal of Venus during the 2001 final, booing Serena and jeering her sister and father Richard Williams when the pair arrived to watch the match.
Richard Williams alleged he had heard racist taunts, and Serena said she was "nervous" when speaking to her father about her possible return.
"He's been through some things when he was growing up," said the 19-times grand slam singles champion. "It was a really emotional time for me when I was talking to him.
"I was like, 'I think I should go back, but I'm not going to go back if you don't want me to.' He said it would be a big mistake if I didn't go back. I thought that was really admirable."
Serena, who plays her opening match at Indian Wells on Friday, also succumbed to nerves when she told her mother about her plans to return to the venue.
"When I was done with my whole story, she said, 'I'll be there for you. Whatever you need, I'm going to be there for you.' I was a little shocked," said Serena. "I don't know why because she has always been so supportive."
(Editing by Frank Pingue)
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