A 16th-minute strike from Hernanes helped the Biancocelesti to all three points at the Stadio Atleti Azzurri d'Italia.
The Bosnian boss, who was taking charge of his first game, said that the team deserved their victory.
"The team fought hard, suffered and created, so I think we were a real team today," said Petkovic. "It is getting close to the image I have of my team.
"I saw Lazio suffering in the first 20 minutes, as we knew Atalanta would be fired up in front of their home crowd. We also needed to shake off the Europa League game played on Thursday, but we created many scoring opportunities and were generally in control.
"At the end Atalanta were raining long balls into the box, but overall Lazio deserved the win."
Petkovic joined Lazio after a temporary spell in charge of Swiss side FC Sion.