Despite Sunday's thrashing, Swansea have a Capital One Cup final to look forward to next week.
Allen said: "I'm not jealous of what Swansea have achieved this season.
"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."