The 29-year-old world number 21 took the first game 12-10 after an impressive trick-shot between his legs with the scores tied at 10-10.
But Egypt's 2014 US Open winner edged the second and third games 11-9 and 12-10 before winning the fourth 11-5.
Simpson had beaten Egypt's Karim Ali Fathi in the opening round.
"Played my first trick shot today. Wanna know how I did it? Me too....," Simpson wrote on Twitter after the match.
Guernsey's Chris Simpson has been knocked out of the US Open, despite pushing world number one Mohamed El Shorbagy in their second-round tie.