Rumours of Zeman's demise have been circulating in the Italian media all week after a terrible run of form has left Roma nine points off the third Champions League spot.
They are without a win in five games since the winter break and remain in eighth place on 34 points, three behind AC Milan who occupy the second Europa League slot.
Hardcore fans in the Stadio Olympico's curva sud began calling from the manager's head after Cagliari's fourth goal, unfurling a banner that read "Boemo (Bohemian, Zeman's nickname) out", before turning their backs on the game.
But Zeman was defiant after the match, saying he will not step down because of one bad result.
"I'm not even going to think about resigning over one game," he said.
"I saw the directors after the game but we didn't talk about specifics, only about a game that went very badly."
Cagliari's victory takes them up to 14th on 24 points after their impressive counter-attacking display.
Radja Nainggolan's smart third-minute goal put them ahead but a thumping free-kick 10 minutes before halftime by Roma captain Francesco Totti levelled the scores.
A terrible mistake from Roma keeper Mauro Goicoechea gifted Cagliari the lead two minutes into the second half when, under no pressure, he dropped Danilo Avelar's cross into the net.
"What can you say about the second goal? In football people make mistakes, and unfortunately this time we made them," said Zeman.
Eight minutes later Marco Sau extended Cagliari's lead when he leapt above his marker to head home Victor Ibarbo's pinpoint cross.
Francesco Pisano compounded Zeman's misery when he calmly tucked home his first goal of the season after Sau's curling shot cracked against the crossbar and fell to the defender.
Marquinho scored an injury time goal for Roma but Zeman will have to work very hard to convince the club's unhappy supporters that the season is not totally lost.
"We played badly, we deserved to lose," added the coach.
"Today there was lots of desire but not a lot of brains. Desire by itself isn't enough and won't ever be enough."
- Sports & Recreation