Zaki had the chance to open the score line in his first appearance in the Cairo derby after only 12 minutes when he stepped up to take the penalty after Tarek Al-Sayed was clipped inside the box.
But the Egyptian international couldn't beat Ahli keeper Essam Al-Hadari, who blocked the effort as Ahli went on to win the game thanks to a brace from Flavio Amado.
"I want to apologize to the fans and I hope they forgive me," Zaki told reporters after Saturday's game.
"I also want to promise them that I will make up for this missed penalty in the upcoming games."
After failing to deliver, Zaki had several attempts on target as he shot from the left and right in the first half before heading from close range late in the game but he couldn't beat the international goalie.
Meanwhile, Zamalek defender Ibrahim Saied rejected accusations that he was responsible for the defeat.
Saied, who was marking Flavio, failed to clear both of the two crosses which the Angolan striker headed into Zamalek's net for the three points.
"We didn't play a man-to-man defense," said Saied, who linked up with his team mates just a couple of days before the game after a trial period with Premiership side Sheffield United.
"I think he was just lucky enough to score twice in this game," Saied said, adding that he was shocked by Ahli supporters' insults through out the game.