Thorsten Fink's side are currently sixth in the Bundesliga, and the former Denmark international is happy with the way things have gone for him since leaving Chelsea.
"Coming to Hamburg was a good decision for me. It has not always been easy, but I was not surprised that it was difficult.” He told Bild.
"When I came we had nine players over 30 years old and we had to change that. We have young team that are on the right track. But the financial foundation needs to be stronger.
"This club have always played internationally, either in the Champions League or the Europa League. HSV are a very big club."
Arnesen went on to say that he does not mind that the club's former players have been critical of the team over the last 18 months.
"If it's not going well I think that's normal. Sometimes they were right. I've got no problem with that."