The influential trio fell out of favor with Shehata for different reasons.
Hamburg forward Zidan was suspended by the Egyptian FA in June for faking injury.
He apparently wanted to be part of Hamburg's pre-season preparations rather than playing for Egypt in their World Cup qualifiers.
"Zidan left us in a crucial time. His presence was needed especially after several of our players were injured," Shehata told Egyptian Radio.
"But he chose to have some rest in order to approach the new season with Hamburg in the best possible way.
"Zidan is suspended by the FA for an indefinite period. He will not return to the national team unless he feels that he committed a mistake.
"He has to be aware that it is a privilege to play for the Egyptian national team."
Ahli's Barakat missed the 2008 African Cup of Nations, citing fitness problems.
But widespread reports suggested that the mercurial midfielder intentionally skipped the tournament which Egypt won in Ghana.
"Barakat refused to play for Egypt in several occasions. He repeatedly asserted that he couldn't play on artificial turfs due to a knee problem," Shehata said.
"But we saw him playing on an artificial turf when Ahli visited ASEC Mimosas in a Champions League encounter, that's why he does not feature in my plans."
Zamalek forward Hamza, who put in some impressive displays in the Egyptian League lately, has also become out of favor with Shehata, who led Egypt to back-to-back Nation Cup titles.
Hamza sarcastically criticized Shehata for consistently leaving him out of the Pharaohs' squad.
"Everybody knows why I do not call up Hamza. I don't want to make any further comments about this matter," he concluded.