Kozac struck twice in the opening 10 minutes before completing his hat-trick at the end of the match, and the Czech has now targeted goals in Serie A.
"This is my first hat-trick for Lazio and of course I am really happy," UEFA.com quotes Kozak as saying. "I am going to enjoy tonight, I am delighted for myself and my team that we have gone through.
"It is not like I give less in the league, I always try to give my best, even if something seems to be lacking in Serie A. Every minute I play, I try to do the same thing.
"We are now into the quarter-finals and all the teams are strong, so it is going to be a great challenge for Lazio, for us and for the fans, and we will give it our best no matter who we face."
Kozak is the Europa League's top scorer with nine strikes.