The Manchester United striker came in for criticism following a muted performance in their opening 2-1 defeat by Italy in Group D on Saturday, with the Daily Mirror reporting he was now battling "to save his World Cup."
Rooney, who was used in a less-favoured left-sided role against Italy, was the only outfield player who started that match to do a full training session on Monday with the other nine only doing a gentle warm-down.
"Sometimes wonder what the press are getting at," Rooney said on Facebook.
"I said from the start I want to do everything I can to make sure I'm ready for these World Cup games and as part of that I was doing extra training a week before the squad joined up.
"That's exactly what I did yesterday, my own extra training because that's what I wanted to do."
For a player who has enjoyed a glittering club career, Rooney's international form has frequently been questioned, especially around major tournaments, where he has struggled to make an impact following an impressive Euro 2004.
Rooney has never scored a World Cup goal.
He has been shunted out of his favoured position in the current England set-up with Liverpool striker Daniel Sturridge occupying the sole central striking role.
He was not lacking in industry against Italy, but often found himself on the margins of the game despite playing a pivotal role in setting up Sturridge for England's equaliser.
England vice captain Frank Lampard urged the country’s media to drop their "fixation" with the striker.
"If people start trying to focus on individuals again and again and again, it can become a bit detrimental. In the squad, behind closed doors, we’re just trying to win games," Lampard told a news conference.
England assistant coach and former Manchester United team mate Gary Neville complained of an English obsession with targeting big players.
"Our country loves it, creating a drama around one player," Neville said on the BBC.
"This time it's Wayne Rooney but that comes with the territory of being an important player in a big nation. I've never known there not be an obsession around one player.
"It was (Paul) Gascoigne from 1996 to 1998, (David) Beckham from 2000 to 2006. From 2006, it was Rooney and Beckham. Now it's Rooney in 2014.
"Unfortunately - or fortunately, because he is a big player - this time it's Wayne Rooney. You can't get him to do a light day's training. That's his character. He just wants to play every second of every day.
"He has an enthusiasm for football that is incredible and he's been like that since the moment I played against him when he was a young Everton kid."
Neville also defended England's display against Italy, saying the poor result was tempered by the quality of the football on show.
"Some of the football was the best I've seen from England in 10 or 15 years in a World Cup or European Championship match," the 39-year-old said.
"As we came off the pitch, we weren't thinking anything other than the team played pretty well, but we got the fine lines wrong."
England face Uruguay in their second group match on Thursday in Sao Paulo.
(Reporting by Toby Davis, additional reporting by William Schomberg in Rio de Janeiro; editing by Ed Osmond)
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