The young attacker was very pleased with his side's win over the Rome club on Thursday, and is eagerly anticipating the last four game versus Antonio Conte's side
Lazio picked up an early lead via Djibril Cisse, but goals from Robinho, Clarence Seedorf and Zlatan Ibrahimovic eventually helped the Rossoneri to a comfortable victory.
"We’re satisfied that we have made it to the next round. It was not easy after going down early on, but we did well to come back," El Shaarawy said to reporters.
"It certainly won’t be easy against Juventus in the next round. It’ll be a battle, but we always aim for the maximum and want to reach the final."
The first leg of the semi-final between Milan and Juventus takes place at February 8, with the return-leg scheduled on March 21.