Ahli's so-called ageing players came under fire after Ahli failed to sparkle in several Egyptian league and Champions League games lately.
Some pundits went as far as calling on the likes of Barakat and Abou-Treika to hang up their boots.
Abou-Treika sat on the bench during Ahli's 3-2 victory over ENPPI on Thursday but mercurial midfielder Barakat notched home two minutes into stoppage time to give the Red Devils their fifth consecutive league win.
"I will not respond to the critics who criticize Abou-Treika and Barakat because those players are the stars and jewels of Ahli," Al-Badri said in a television interview after the game.
"Abou-Treika didn't play today for technical reasons, he is neither injured nor have physical problems.
"But we also have to take into consideration the fact that he has been playing for years without sufficient time to rest."
Abou-Treika joined Ahli in January 2004 and Barakat followed suit few months later as the Cairo giants began a rebuilding process after a barren run.
They went on to become the pillars of a dominant Ahli side that won a host of domestic and continental titles during the past six years.
Ahli's last-gasp win over ENPPI moved them up to second with 17 points from seven games as they maintained their unbeaten run in the competition.
They are just one point behind leaders and arch-rivals Zamalek, who played two games more.
"This win is very important, we don't want to drop points following our Champions League elimination (at the hands of Tunisia's Esperance in the semi final)," Al-Badri added.
"ENPPI were a tough opponent so I'm happy with the result although I know the performance wasn't that good."