The 1997 Lions, with Martin Johnson, Neil Jenkins, Scott Gibbs and Jeremy Guscott, have gone down in rugby folklore.
And having come agonisingly close to replicating the success in 2009, Jones insists only a series triumph will do Down Under.
"It is not about the individual Tests, and it is not about winning all the games on tour," said Jones.
"If you have to suffer a loss in the provincial games in order to get a Test series win then no-one will remember that loss.
"It does not matter if you win a Test, you want to win the series - because no-one remembers a Lions tour if you do not win the series.
"I will never forget Paul O'Connell saying that last time in South Africa.
"If you want to be up there with the likes of Willie-John McBride and the rugby royalty those types of players are, then you have to win a Test series in the southern hemisphere.
"I remember the Tests which are the crescendo of everything that has gone before."
Jones is one of 15 Welshmen in Warren Gatland's Lions squad, which will be led by Sam Warburton.
The Ospreys skipper has backed Warburton's captaincy and reckons he will get an abundance of support from previous leaders Paul O'Connell and Brian O'Driscoll.
"Brian O'Driscoll and Paul O'Connell have got a huge wealth of experience," added Jones.
"Not every player will play every game. It's going to be tough to ask any player to do that and Sam's just the same. I don't think he'd expect to play every game, plus you need that extra ability to use the best out of people around you.
"And I think Sam will be able to do that by employing the likes of Brian O'Driscoll and Paul O'Connell and the experience they've had and the experience of previous Lions tours.
"Knowing Paul O'Connell and guys like that and the professionalism they display when they are captain, they'll just display it by being led by another man."