The Three Lions coach took over from Rafael Benitez at Anfield in the summer of 2010 but was sacked in January 2011 after a dire run of results.
"How could I [not have regrets]? I went to Liverpool with the intention of spending a long time there and helping to build the club up like I've seen it built up now," The Mirror quotes Hodgson as saying.
"I wasn't able to do that, so I regret it and I'm sad about it. But it can happen when the people who appoint you are not the same ones who dismiss you.
"I knew, when I took the job, the club was in a period of transition. I realised it might not be too easy just to walk in and wave a magic wand to turn it around. New owners come in, they might have other ideas. I'm just fortunate that what has come up since, with England, has been good for me."
Friday's World Cup draw saw Hodgson's side grouped with Uruguay, Italy and Costa Rica.