Zeman said that his team did not press forward enough and were "content in possession" for large periods of the match.
The Czech coach also believes that some of the younger members of his squad may have been affected by the brimming atmosphere.
"Altogether it wasn't a great performance," said Zeman. "Especially in the first half when we were too slow, not aggressive and never went forward on the counter-attack.
"We were content with possession, which was a great shame. Passing the ball horizontally is pointless and it allows our opponents to get settled in. If we don't speed it up and shake off our markers in midfield, then we'll go nowhere.
"We had five debutants tonight and seeing the packed Stadio Olimpico does affect young players, but in the past six weeks we have worked on something very different to what was seen tonight."
Zeman is enjoying his second spell in the Italian capital.