The All Blacks great, who values the tour alongside playing at the World Cup, destroyed the Lions, scoring 33 points and crossing for two tries with a masterclass at first five-eighth to win the second test 48-18 in Wellington to secure the series.
Carter had just 18 tests to his name prior to that Lions series and admits he didn't appreciate the significance of the tour until facing questions from British media.
"I remember it started in 2004 when the All Blacks toured the northern hemisphere in the autumn series [in November and December]," Carter told ESPN.
"Doing media before a test match, normally it's about the game that Saturday, but a lot of the questions were about the Lions series the following year.
"All of a sudden, I realised how big a series it was going to be."
Carter, who top-scored in the 2005 series with 44 points, played in the first and second tests but missed the third through injury as the All Blacks won the series 3-0.
The Lions have their first chance in 12 years to avenge that series defeat when the first All Blacks test of their 2017 tour starts at Eden Park on Saturday.
"Something I was a little bit naive about was exactly how important and how much of a following these Lions series got. I didn't really understand the intensity of the series," Carter added.
As a member of two All Blacks World Cup winning squads, Carter fulfilled a dream that all rugby players hope to achieve in their careers.
But he rated playing the Lions alongside featuring at a World Cup, with the All Blacks having won the last two tournaments in 2011 and 2015.
"I was extremely grateful to play in a Lions series early on in my career," Carter said.
"As much as people talk about how big and important the Lions series are as they only happen every four years, for us it's even more so as it's once every 12 years in our country.
"It's definitely ahead of anything you play as an All Black, except potentially a World Cup because there's a lot of history that goes into a Lions series, which makes it a lot more exciting."
Photo: REUTERS (Dan Carter attempting to escape the clutches of former Lions flanker Lewis Moody)