The victory secured Udinese Serie A safety and sent Frosinone down.
The goal was Davis' first in Serie A and the former Aston Villa striker said: "My first thought is to thank God, without his help it wouldn't have been possible.
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"I have to thank my teammates, I suffered injuries during the season and I dedicate this goal to them."
"I'm speechless, I see the fans celebrating: they supported us at every moment of the season, at home and away. It's for them."