Zeman sees Roma as a work in progress
Goals from Alessadro Florenzo, Pablo Osvaldo and Marquinhos earned visitors Roma all three points at the San Siro.
And after earning his first league victory back in charge at Roma, following a 13-year absence, the veteran coach praised his team's performance, but wants to see more from the players as the season develops.
"We played a good match, the team definitely wanted to counter Inter and at times we did that well," Zeman said.
"This result should give us belief, even if we still have room for improvement."
On bitter rivals Lazio's perfect start to the season, he replied: "I have to think of Roma. Next we play against Bologna, not Lazio."
Inter coach Andrea Stramaccioni was disappointed with his team's second-half performance, questioning the mental application of his players.
"I did not like the second half, we had a great first half and then the goal by Osvaldo, on a long ball from Totti, found (us) a little unprepared - (It was) a lightning (quick) restart," he said.
"Following the second goal, (we were) not good. This should make us reflect. Something has not gone right on a psychological level tonight."