The 23-year-old, who joined from Swansea City in the summer, had struggled with a shoulder injury for much of the season before surgery brought a premature end to his campaign last month.
"The fans have definitely not seen the best of me yet," Allen told the club's official website.
"It's no secret that recent months haven't gone great for me. I am confident and faithful that next season I can perform a lot better."
Liverpool signed the Welsh international for £15m from Swansea on a long-term deal.