Silva's three-goal haul at the Ernst-Happel-Stadion has made him the first Milan player to score a European hat-trick since Kaka in 2006.
"It was my first start in the Europa League, I got a hat-trick and am very grateful to my teammates. We put in a great performance," Silva told Sky Sports News.
"I felt good alongside [Nikola] Kalinic. I'm happy to be part of this squad and get along with all my teammates, as we give our best for each other.
"The coach (Vincenzo Montella) will decide if I am ready to start in Serie A. I work hard and we are all fighting for the same team objective."
Up next for Milan in the Europa League is a game at San Siro against Croatian giants Rijeka on Thursday, September 28.