The young forward was impressed with the Slovenia goalkeeper's performance, and was delighted with his goal against the Rossoneri's arch-rivals
The Italy forward gave the Rossoneri the lead before the interval and Mario Balotelli had a number of chances to extend their lead.
However, Handanovic kept his side in the game with a string of fine saves, before Ezequiel Schelotto eventually restored parity in the second half.
"In the first half we created a lot but Handanovic played a fantastic game and made some really great saves," El Shaarawy was quoted as saying on the Milan website.
"The result was a bit disappointing as we deserved to win based on how we played."
El Shaarawy then went on to voice his delight with his goal, and stated that scoring in the derby is a unique feeling.
"It was a great ball from [Kevin-]Prince [Boateng] that set me up. I’m happy with the goal as scoring in a derby is a really unique experience.
"I will watch the goal again and again, it was a moment of great satisfaction."
The youngster picked up a minor knee injury in Sunday's draw, but stressed that the knock does not appear to be too serious.
"My knee is a bit sore but I’m sure we’ll be able to take care of that."
Milan sit third in Serie A at the moment with 45 points from 26 games.