Frey was delighted to get one over a French club and see Fiorentina progress to the knockout round.
"I was very motivated and it is an immense joy to qualify, as few expected us to manage it with this group," grinned the Fiorentina goalkeeper.
"We have matured from last season, changed a few players and were able to make the most of home advantage. That was crucial in this group. Mistakes are made to be analysed and eradicated."
The 1-0 win over Olympique Lyonnais put the Viola through to the final 16 for the first time in their history.
It was also the first time in 10 seasons that Liverpool have failed to advance to that stage.
"I have made history with Fiorentina, so it is a wonderful moment for me and my club. We really wanted to make an impact on Europe this season and we achieved it.
"I have to single out Vargas, who has surprised me. He has been extraordinary this season with his mental and physical strength. He is on stunning form."