The Biancocelesti slipped out of the European places towards the end of the Serie A season and suffered the ignominy of seeing bitter foes Roma climb above them to snatch sixth place on the final day.
As a result, the first ever Rome derby to contest a cockade offered much more than the usual bragging rights, with the final Europa League place also up for grabs at the Stadio Olimpico.
Roma were desperate to win a 10th Italian cup and add a permanent silver star to their shirts but it was not to be as Senad Lulic gifted Lazio the trophy with his 71st-minute tap-in.
Petkovic, who only moved to Italy last June, told the La Repubblica: "It is a victory we deserve for all the hard work we did this season.
"The players deserved it for all the application and sacrifices they made throughout the year. I knew the preparation we did over the last few days would pay off.
"The lads gave their hearts and souls. We could perhaps have done better on the counter-attack, but it doesn't matter any more.
"Credit to Roma, who deserved to be in the final. I know how they are feeling, I've been through these kind of moments and I'm sorry they're suffering. But that's football."
A nervous encounter in the Italian capital was wide open for over an hour with players on both sides wasting numerous chances to make the breakthrough.
Goalkeeper Bogdan Lobont had been a tower of strength for Roma until he flapped at a Antonio Candreva cross to tee up Bosnian winger Lulic at the far post.
"I will never forget this victory," Lulic said. "To have been the one who scored is incredible.
"I saw Candreva coming from deep on the right and raced to the far post, where I found myself in the right place at the right time. It was a beautiful moment."
Roma's forward line were particularly profligate with the usually reliable Francesco Totti out of sorts until he rattled the crossbar late on, and young striker Mattia Destro struggled in Pablo Osvaldo's usual starting berth.
Giallorossi interim boss Aurelio Andreazzoli is now expected to make way for a permanent appointment and he admitted his team selection let the fans down.
He told asroma.it: "Why did I pick Destro over Osvaldo? That's something I would go back and change, without a doubt.
"The game was horrible. We didn't do any of things we'd practised. There were errors in our movement and in possession, especially in the early stages.
"Then when it looked like we were going to take the lead in the second half, Lazio benefited from a totally random event like the deflection of the ball off Lobont and on to Lulic's feet.
"It is with regret and some bitterness, however, that we must accept what happened."