The Merseysiders sit in 14th place in the table after winning just one of their opening seven league games.
"With change at a football club it does take a while for things to embed and settle in.
"Liverpool is full of world-class players and I'm privileged to play alongside them. I'm looking forward to a successful season.
"You can really see the style of play is coming into its own. The performance at Norwich typified that so I'm looking forward to the club climbing up the table."
"To get the chance to move to a club like Liverpool was a great opportunity. I've really enjoyed my time there so far and am looking forward to the future with the club."
Allen added: "The price tag is going to add pressure, but that is something you come to expect as a football player."