Allen joined manager Brendan Rodgers in making the switch to Anfield for around £15m and insists that he is not jealous of Swansea's achievements this season under Michael Laudrup.
The Swans could win a trophy next weekend when they face Bradford City for the League Cup.
"I'm not jealous of what Swansea have achieved this season," Allen, who may start against his former club on Sunday, said.
"I left a club last summer I loved massively but I closed that chapter of my career. This is a new chapter for me here and I am looking forward to creating new memories and achievements with Liverpool.
"Swansea have got their chance to play in a cup final coming up but I'm hoping that during my time at Liverpool I'll get the opportunity to do that a few times myself."
Swansea are currently two places and one point above Liverpool in the Premier League.