The Three Lions were big favourites heading into the summer clash, and recorded a 3-0 victory over the course of five matches.
However, Anderson feels that England were fortunate to win by such a convincing margin and believes that the winter series will be a lot closer.
"All four games were tight and could have gone either way. 3-0 probably flatters us a bit if we are being brutally honest," Anderson told the Daily Telegraph. "But at the same time we fought out of holes and that is what you need in a series like this one. It might not be pretty but it is huge for us and we really want to win.
"We would take any win at all. We would take a 1-0 if we have to. I imagine it will be close. I think the 3-0 this summer was a closer series than 3-0 suggests. We are going to have to be prepared for them coming hard at us. We have to be prepared for the media going after us and probably the whole country.
"We know what will be thrown at us. There is always niggle in the media, ex-players coming out with things. One part of our success last time was dealing with that. As much as we are looking forward to going to Australia to play cricket it is an amazing country to tour and we are going to make sure we enjoy the whole trip."
The winter clash gets underway in Australia in November.