Agger appeared to question Hodgson's methods in stories published in Denmark on Tuesday morning, in which the defender was quoted as saying he was "here to play football and not to unload [the ball]."
But Agger says his apparent rejection of Hodgson's philosophy was instead a response to a question put to him by a televsision reporter, and subsequently twisted by the Danish press.
"I am very disappointed with the papers in Denmark for the way they have done this story,'' Agger said. "I spoke to Danish TV after the game on Sunday and answered the questions that were put to me. I didn't speak to the papers.
"The problem was the questions never appeared on TV, only the answers did, and then the newspapers put their own questions in. What came out was 100% wrong and that is why I am very disappointed.
"The TV journalist asked me what I needed to do to get back into the team and suggested I should start hitting more long balls. I said I wouldn't do that because I'm not that kind of player. That's where that quote came from.
"I actually think we play good football and that we have showed that against Manchester United and against Arsenal. What I don't understand is that it was only a few days ago when I spoke to the media ahead of the Steaua Bucharest game and said everybody at the club was happier now with the new manager, the new players and the new methods.
"It's strange to read this just a few days later but that's the way the media works, especially in Denmark. I have been involved in every [Premier League] game this season. Of course I'm disappointed when I'm not in the team, but I have been here for five years and really like it here.
"I wouldn't have stayed for this long if I didn't like it or if I was unhappy. I am still happy and will keep fighting for my place."