Allen spent five years in South Wales before following manager Brendan Rodgers to Anfield in the summer.
And the midfield schemer admits it was emotional going "home" to the Liberty.
He added: "It was exciting for me to come back.
"I had some great years here, Swansea have great support and there's a great bunch of lads in the dressing room as well, so it was nice to come home.
"Playing in midfield against Leon Britton was a strange but good experience as he has been something of a mentor to me, so it was a great challenge against a great player.
"Swansea was an incredible experience in my life and I can't be more grateful to this club. The ride they have been on has been an amazing story and to be part of that I feel very humbled and privileged.
"I'm in a new chapter of my life now at Liverpool and am loving life here. It's an incredible club to represent and I'm loving every minute of it."