Virtue was an U23s captain at Liverpool before making the move across to Bloomfield Road in January 2019.
He is joined by Critchley - his former U23 coach - who took over the League One club in March last year.
"As some Liverpool fans will know, Neil Critchley is the manager, so football is a small world and I'm definitely enjoying my time there.
"It's been a bit of an up and down season because I had an injury but I got back to playing games and enjoying my football. It's what every player wants: to play games, get better, improve, and that's what I'm hoping to do."
And on working with Critchley, Virtue added: "That was just crazy. I had a few days off and he text me saying, 'Enjoy a few days off because I'll be seeing you on Wednesday!'
"I saw him in the running for it but I thought he enjoyed being a youth coach. But seeing him getting the Blackpool job was just amazing for me."
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