The Egypt's all-time leading scorer, who is renowned for his dedication and enthusiasm to work, broke down after Zamalek threw away a 2-1 lead in the dying minutes of the game.
FilGoal.com's Hossam Adel in Alexandria said Hassan's emotional reaction following the disappointing draw saw him rip his T-shirt.
He also felt dizzy after Zamalek extended their winless streak against Hodoud to five matches.
A first-half penalty from striker Ahmed Hassan Mekki gave Hodoud the lead but Ivorian striker Abou Kone scored on his debut with a superb overhead kick to level the score early in the second half.
Amr Zaki put Zamalek in front in the 62nd minute after converting a penalty but Zamalek could not hold onto their narrow advantage.
Hodoud midfielder Mohamed Hamed notched home with three minutes remaining to secure a share of spoils.
Individual Mistakes
"Some individual mistakes allowed Hodoud to claim a draw," Zamalek football director Ibrahim Hassan, the twin brother of Hossam, said after the game.
"We were better throughout the game but we wasted too many goalscoring opportunities.
"But we need to put that result behind us immediately. There is a long way to go, this is just the beginning."
Hossam Hassan is keen to help Zamalek win their first league title since 2004 but they are likely to face fierce competition from arch-rivals Ahli, who strengthened their squad with several high-profile signings.
Zamalek finished as runners up behind league champions Ahli last term under the guidance of Hassan, who turned around their fortunes after replacing French coach Henri Michel in the second half of the season.
Hodoud exploited the weakness of Zamalek's right-back Ahmed Ghanem to launch many raids on keeper Abdul-Wahed Al-Sayed.
A lapse of concentration from Ghanem, who was on the verge of leaving Zamalek in the summer, helped Hodoud earn a penalty which gifted them the lead shortly after the quarter-hour mark.
"We wanted to substitute Ghanem because he looked out of form but we couldn't because we had to replace other players after they got injured," Zamalek assistant coach Tarek Soliman told the post-match news conference.
Ghanem was the only recognized full-back at the White Knights' disposal as Hazem Emam and Omar Gaber were missing.
Emam is yet to complete an eight-match ban for losing his temper in a league game last season while Gaber is on international duty with Egypt's U-20 team.
"I want to ask the Egyptian FA a question. Which is more important, a friendly game for Egypt's youth team or a league game for Zamalek?" Soliman added.