Pictures of the bash were released by local media last month, showing many celebrities dancing with Fadali.
Zaki was among the attendees and although the photos did not show anything inappropriate, he was criticized solely for his presence.
The conservative Egyptian society usually blames the public figures, especially footballers and politicians, for attending such parties.
"People should criticize for my performances on the pitch, not anything off it," Zaki said in an interview with Dream TV on Saturday.
"Any football player has his own personal life and freedom as long as he fulfills his commitments with the club.
"I never skipped a training session or training camp with Zamalek. I'm accomplishing all my duties as a player.
"I would have avoided being photographed during the birthday if there had been anything inappropriate."
Fadali was quoted as saying that Zaki phoned her to express his anger over the photos which were taken.
Zaki is currently nursing a knee injury that forced him to sit out Zamalek's 2-0 Egyptian Premier League victory over Police Union and 2-2 draw at Gaish.
He said he would fly to Germany in the next few days to find out the exact reasons for the niggling problem.
Zamalek coach Hossam Hassan will be hoping to have the combative frontman, who has scored three league goals so far this season, available for the anticipated Cairo derby against arch-rivals Ahli on November 26.