The usually glum-looking Eid was sent off in Hodoud's 2-2 draw with promoted side Smouha on Thursday after pushing the referee's hand while the official was about to hand him a yellow card.
Eid waved his arm in protest at referee Medhat Al-Houfi's decision to book him, causing the yellow card to fly away.
He faces up to a six-match suspension for his action that earned him criticism from local media.
"I'm worried that any punishment I get may cost me my Egypt place," Eid told Modern Kora.
"I swear I did not mean to push the yellow card from the referee's grasp, I just wanted to know his reasons for cautioning me.
"The referee was raising the yellow card when I waved my arm so it was accidental. I tried to explain that to him afterwards because I know I might be heavily punished."
Eid has been a regular member of Egypt's squad since coach Hassan Shehata took over late in 2004.
Although he is mainly used as a substitute, the 30-year-old's presence always makes the difference.
However, he is consistently criticized by Shehata for failing to control his temper during matches.
"I want to apologize for the referee and all fans for what happened on Thursday," he added.
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