The Biancocelesti went into the match having not won their last six league fixtures, but a double from Klose gave them all three points at the Stadio Olimpico.
"We dominated the first half and deserved to lead by more than 2-0," Petkovic told Sky Sport Italia. "After the break we got afraid and our legs felt rather heavy, but I must compliment the lads for pushing through it. They worked hard, did not concede and scored goals, so it's a definite improvement.
"The side was certainly determined and I never had doubts about that. They always gave their all, but needed that extra bit of 'rage' to finish off chances and we had that today.
"With the right spirit you can provoke certain incidents to go your way and earn your own luck. Klose brings something more to the side and that makes everyone raise their game, so with a champion like him everything becomes easier."
Lazio are currently eighth in the Serie A table.