Messi was ruled out of the game due to a hamstring injury and decided to skip the post-match celebrations after the 2-1 victory in Paris.
The Argentine was only 18 at the time and was still trying to make a name for himself in Frank Rijkaard's star-studded side. He had scored only nine goals for the Catalan giants at the time, and has now reflected on his decision to miss the celebration.
Speaking to AS, he said: "I'm sorry I didn't [go out]. I didn't realise what was happening. At that moment I was thinking about not having played. At least I would have liked to be on the bench that night. Until my injury (tear against Chelsea in the round of 16), I participated in every Champions League in my career.
"I was disappointed. I deeply regret that episode. We won that Champions League and I was not sure what would happen again because it is a difficult competition to win. Fortunately, I had the opportunity to enjoy it."
The Paris Saint-Germain star added he would like to "go unnoticed" by fans and enjoy some quality time with his family. He said: "I have been Messi for 34 years, so I am starting to get used to it. I am happy with everything that has happened.
"Although sometimes I have to admit that I would like to go unnoticed, enjoy my family without people recognise me. I do not complain, on the contrary, it is always nice to receive a compliment, a smile or someone who asks me for a photo. I am used to it and for me it has become normal. So very good."
Messi won his record seventh Ballon d'Or last month, finishing ahead of Robert Lewandowski and Jorginho.