Having characteristically set his side up to attack from start to finish, the Giallorossi coach was dismayed as Rolando Maran's Elefanti took the lead twice through Giovanni Marchese and Alejandro Gomez.
An acrobatic scissor kick from Pablo Osvaldo and a dramatic late equaliser from debutant Nico Lopez allowed the hosts to take a point, but Zeman had protested vehemently as Marchese tapped home the opener from what appeared to be an offside position.
The referee ruled Roma striker Osvaldo had deflected the ball into the Catania man's path, and allowed the goal to stand.
Gomez capitalised on a defensive mix-up to nudge the Rossazzurri back into the lead after Osvaldo's equaliser, with Zeman once again pleading for offside.
He told the club's official website: "I'm bitter about the points we lost, mainly because the two goals we conceded were offside.
"I'm sorry about the result, and that the performance could have been better.
"We tried different things in training but I don't know if we were too nervous or scared of losing the ball.
"Our problem was that the wingers failed to cut inside enough."
After winning promotion with Pescara this summer, Zeman was re-hired at the Stadio Olimpico after a 13-year absence.
He added: "It was great to be back at the stadium and I was happy to see so many people at the Olimpico.
"I've always provided football 'for the people', to entertain them and make want to come and see football.
"I hope the people come to the stadium for that reason - to enjoy themselves."
Catania boss Maran was making his Serie A debut as a coach having replaced Fiorentina-bound Vincenzo Montella in June.
He told Sky reporters after the game: "With regret, we leave with a draw.
"We played well at a difficult place. It's a shame about that goal at the death, but the end of the game was so intense that we were always vulnerable to errors."