With just one match remaining in the group stages, the Egyptian champions are on the verge of booking their spot in the last four.
But despite Al Ahly holding the Group B lead, they also know defeat on Saturday could knock them out of the competition given the close nature of the pool.
Al Ahly – top with eight points from five matches – host the bottom-placed Etoile Sahel on Saturday.
"We are the biggest club in Africa. We have to win," Garrido said.
"We are under a lot of pressure to win and we will try to do just that."
Al Ahly lost 1-0 to Nkana of Zambia in their last group match – Garrido's first continental fixture in charge of the club.
And the former Villarreal coach said he learned "many lessons" from the clash as Al Ahly missed a chance to seal their last-four berth.
"Our match against Nkana was my first on African grounds," he added.
"I could say that Nkana's pitch was the worst thing I've seen in my coaching career."
While just one win separates Al Ahly and Etoile, Nkana and the Ivory Coast's Sewe Sport are only one point apart.
They host Ivory Coast's ASEC and are full of confidence after a 4-0 win at Cotonsport earlier this month.
