After enjoying the initial relief and celebrations immediately after hearing his name read out by Gerald Davies on Tuesday afternoon, the Wales prop now insists he wants to set the record straight ahead of next month's tour to South Africa.
"2005 was a great experience for me but it's unfinished business because we didn't win the series," Said Jenkins, who played in all three internationals in New Zealand four years ago.
"Paul O'Connell was the only other forward to start that first Test against the All Blacks and he will say the same."
While O'Connell's position as Lions skipper in 2009 makes his position in the Test XV more than likely, Jenkins is one of a handful of other names already been touted as an almost certain starter.
The 28-year-old Cardiff Blues star has been in superb form so far this season, earning rave reviews for his work rate and tackle count as well as his efforts in the set piece.
Having toured alongside O'Connell in 2005, Jenkins has developed a good friendship with the Munsterman.
Now he hopes O'Connell's winning mentality and determination to succeed will rub off on the entire Lions squad as they search for a series victory over the world champion Springboks.
"Paul is a great captain and a great competitor - you can see that from the way he plays for Munster and Ireland," added Jenkins.
"We became very good friends when we toured together in New Zealand and I've got a lot of respect for him both on and off the field.
"It's great to be in the squad but when you go out on the tour, the main goal is to be in the Test team."
Double Grand Slam winner Jenkins is joined in the 2009 Lions squad by fellow Welsh front rowers Adam Jones and Matthew Rees.
He would love to see a trio of Welsh Test starters at prop and hooker, particularly after the criticism the Welsh scrum faced during the early stages of Jenkins' international career.
"It's great to see Adam and Matthew also included in the squad. I was the only Welsh front five player in the squad last time so I hope we can all make an impact this time around."