Inzaghi's job has been the subject of great debate in recent weeks, with Milan languishing in 11th position after 22 rounds of Serie A.
Saturday's 3-1 loss at leaders Juventus left Milan with just one win from their past seven league fixtures, increasing the pressure on Inzaghi.
But El Shaarawy, who is no closer to a return from a broken metatarsal after revealing he will remain in a cast for another three weeks, said while results are not ideal, the players are united behind the 41-year-old.
"The coach is giving his all, just like the team," El Shaarawy told reporters. "We have great faith in him.
"He's a great coach and a wonderful person. We are all with Inzaghi.
"It is not an easy time, but we have to unite as a team and be more aware of our capabilities.
"We must take it one game at a time. A month ago we were seen as Champions League candidates, now as if we're heading for relegation.
"We just have to focus on doing our best."
