The Giallorossi were two goals up through striker Erik Lamela in the first half, but Maurizio Domizzi took advantage of sloppy defending from a free-kick and an Antonio Di Natale double - his second from the penalty spot after Leandro Castan had ruled to have fouled in the box - ensured the completed comeback.
The Czech coach believed the decision to award the spot-kick was incorrect and also alluded to Catania's 'goal' in what has been a controversial weekend in Serie A.
"After seeing the replays, I don’t think it was a foul for the penalty. It has been a bad weekend for referees. People say they don’t decide league, but I think on the whole they really can," Zeman told Sky Sports Italia.
"We started very well, creating another three great scoring opportunities along with the two goals in the opening half-hour."
Nevertheless, he did acknowledge his side’s weaknesses, adding: "If you don’t attack the ball straight away then you have problems. Udinese played very well on the counter-attack and we were unable to stop them."
The result means Roma are now sixth in Serie A with 14 points, eleven behind leaders Juventus and with the joint worst defensive record in the league.