A first-half mistake from Milan goalkeeper Christian Abbiati saw the visitors take a 1-0 lead but the 18-year-old struck in the 64th minute and eventually gave the San Siro club a share of the points.
El Shaarawy told the club's official website: “It is an indescribable thing scoring goals, it was a unique experience in front of the fans.
"I felt great emotions tonight, I feel sorry about the draw, but we played a great game.
“I hope the coach will give me more opportunities to prove my worth."
The goal is the youngsters first in just two appearances for Milan after joining from Genoa in the summer.
Massimiliano Allegri's side, however, remain without a win in Serie A after three matches and they play host to Cesena this Saturday.