The 22-year-old Wales international joined the Reds from the Welsh club this month for a record-breaking £15m transfer fee.
Allen developed at Swansea's youth academy and says that he will forever love the club.
"I've got a massive attachment with Swansea and that won't change," he told WalesOnline.
"I was with the club during its lows, when there was the chance the club could have dropped out of the league and a danger of whether we'd even have a youth set-up for me to be in.
"It's the only club I've known and then, on top of that, things had been going so well. It would be difficult for anyone to leave something they love."
However, Allen is looking forward to a new chapter in his life playing for Liverpool, and is awed by the prospect of lining up alongside club legend Steven Gerrard.
"These are guys – like Steven Gerrard – who I've watched for years and years and never even dreamed of playing against them, let alone with them," he explained.
"From that side of things, from an opportunity point of view the decision to move was pretty simple. There's the mixed emotions, the low, of leaving Swansea but I've always dreamed of joining a club like this. I've described it as a difficult, easy decision.
"The quality at the club is exciting and I can only see it benefiting my game."
Liverpool will begin their Premier League campaign with an away game against West Bromwich Albion on Saturday.