The Nerazzurri captain was disappointed with the team's display and revealed they will only analyse what went wrong in Tuesday's training
The San Siro outfit were nowhere to be seen, as single goals from Juan and Bojan Krkic, either side of a Fabio Borini brace, gave coach Claudio Ranieri a nightmare return to his former club.
"I think this was Inter's worst performance since the start of the season, regardless of the fact that Roma played very well and deserved to win," Zanetti told Inter Channel.
"We did not even turn up, it was a mass blackout, but we have to try and remain concentrated for Sunday's game because we can't repeat a performance like today's.
"Roma deserve full credit. They kept hold of the ball well and were able to pass their way out of defence and that's when we started struggling."
Zanetti then revealed that his side did not analyse or discuss the defeat after the game.
"We will talk about it on Tuesday because lots of things can be said in the heat of the moment after a game like that," the Nerazzurri captain explained.
"I do not like to discuss a game with the other players right after the final whistle.
"We are all bitterly disappointed right now, if we start looking for more things to hurt ourselves with it will only worsen the situation."
Inter remain fifth in the Serie A standings, nine points adrift of leaders Juventus, and could be caught by Roma, who have one match in hand.