The Wales international moved to Merseyside from Swansea City last season but missed the end of 2012-13 after undergoing surgery in March.
However, the 23-year-old has now returned to full fitness and says that he cannot wait for the start of the new season.
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"Having missed the end of last season, I personally couldn't wait to get back in. Hopefully I can put the injury behind me once and for all.
"I think, for anyone, your first year at a new club can be tough in some ways but I feel settled here now and I'm looking forward to a fresh start with the coming season. Hopefully I can put in some good performances.
"I think last season I may have put myself under too much pressure. So it's a case of just giving my best every day in training and in every match. That's all I can do, really."
The Reds have been busy in the transfer market this summer, bringing in Iago Aspas, Kolo Toure, Luis Alberto and Simon Mignolet and Allen reports that the news faces are looking good.
"They've settled in really well," he added. "With new signings you sometimes worry that it might take them a little time to adapt but they've settled straight in and they've got into the swing of things straight away, which is a really, really positive sign."