Federico Balzaretti and Adem Ljajic scored second-half goals, while Lazio's Andrea Dias was sent off late on, to give the Giallorossi the Rome derby bragging rights and send Rudi Garcia's side top of Serie A.
Petkovic lamented his team's bad luck after the loss but said Roma deserved to take all three points, with the defeat leaving Lazio in eight spot in the table.
"I think that maybe Roma believed a little bit more and dared a little bit more which is the only disappointing thing for us," he said.
"However, they only had more belief after they scored their first goal and we made too many mistakes. Even if we were only 10 men, we managed to believe until the end that we could get something from the match.
"With Ederson's chance late on, we could have changed the result to 1-1, but at the end there was that penalty kick (from Ljajic).
"Roma totally deserved this result and I congratulate them, but we could have changed the result if we managed to be luckier and more committed."
The 50-year-old said Balzaretti's 63rd-minute opener was the decisive blow and felt the result could have been different had his side taken their chances early on.
"The match was decided by the team scoring the first goal. Until the result was 1-0, we had a lot more chances to score goals and we could have changed the result," he added.
"I feel we were also the better team at the beginning of the second half because we started in a more offensive way.
"In the first half of the match we controlled the game, counter-attacked when necessary and caused them difficulties.
"They're a good team and they keep the ball well, which is a credit to them."