The Manchester United striker has never scored a goal at the tournament in eight games, but has notched five times in six outings in past European Championships.
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"Apart from my first tournament at the 2004 Euro Championships, I would like to have played better and hopefully I've still got an opportunity to do that this time around," he told Times Of India.
"To be honest, I don't feel [the pressure]. Sometimes it might look like that. But I don't think: 'I have to try too hard' to make us win.'
"I do hear all that stuff; but I don't take much notice of it. There are 23 players in the squad and there's competition for places which brings the best out of the player. It's not about me."
"[I am] very determined [to be a star at the World Cup]. That is what I have wanted to do in all the other tournaments and it hasn't happened. I want to do well and I want to try to help England be successful.
"So [there is] no change, there will be no added pressure. I won't put any added pressure on myself but obviously I want to try to perform and that is what we all have to believe we can do."
When asked if he has unfinished business at the World Cup, he replied: "It's not just me! Every England player since 1966 has. You have always been regarded as one truly world class player on who England's hopes rest."
England start their World Cup campaign against Italy on Saturday, before facing Uruguay and Costa Rica in Group D in a tough-looking set of fixtures - but Rooney is refusing to set a target for the team.
"I don't know. We'll speak about our own targets behind closed doors and I'm sure the press will have a target which they think we should be doing as well. I'll let other people decide what they think," he said.