The cup holders were ousted from the competition's round of 32 after slumping to a 1-0 defeat to third-division side Bani Obeid.
Al-Hayat sports presenter Ahmed Gamal pointed the finger at Zamalek's stars for the dismal show before highlighting Hamza's error that led to Bani Obeid's winner.
"What happened this afternoon is illogical," he said during the channel's post-match analysis.
"Zamalek have many stars who earn millions of pounds, yet, they lost to a relatively unknown club.
"Bani Obeid's sole goal came as a result of a blunder from Hamza, who was dispossessed in midfield."
Angry Response
The 27-year-old hit back at his namesake Gamal with an angry response.
"What you are saying is nonsense. You are trying to stir the fans' wrath towards me," he told Gamal in a telephone interview.
"I was dispossessed, so what? Does the player who earns millions of pounds can't lose the ball?
"It is normal that we lose against Bani Obeid. They were better and deserved to win."
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