England were humbled on home soil in 2015, finishing third in Pool A, with Wales and eventual runners-up Australia securing progression to the knockout stages.
On Monday, Vunipola was included in Eddie Jones' 31-man squad for the upcoming tournament having starred in Sunday's 33-19 defeat of Six Nations champions Wales.
Despite their disappointment in 2015, Jones' side will be favourites to progress from Pool C, with France, Argentina, United States and Tonga their opponents, and Vunipola does not believe England's failure in the last World Cup will haunt them in Japan.
"That was done four years ago. As soon as it was done it was old news," Vunipola told Omnisport.
"For us, it's about creating our own legacy and we managed to do that after the World Cup. We managed to win the Six Nations [in 2016 and 2017] and we need to believe that we can be successful and that it’s within our grasp.
"I put it quite bluntly, but I truly believe it, I truly believe we can win the World Cup."
4' ENG 7 - 0 WAL
— England Rugby (@EnglandRugby) August 11, 2019
However, Vunipola is wary of underestimating England's pool-stage opponents.
"It's important that we focus on England, and I'm sure we don't [underestimate the opponents]," Vunipola added.
"It showed when we played teams like Italy that people think that it will be a banana skin for us, we took them as seriously as everyone else.
"We don't go into internationals thinking we can never lose as you saw with Scotland, it's just a non-starter for me that one."
Vunipola was speaking at a coaching session he was leading with fellow Saracens and Harlequins players on behalf of Land Rover at Beaconsfield RFC.
Photo Getty Images Caption: England's Billy Vunipola in action against Wales