Despite a sluggish start to the season, the Lazio boss does not feel the German's goal which led to victory against Cagliari spared him the axe at the weekend
The Germany veteran broke the deadlock early in the second half before Antonio Candreva doubled the advantage within minutes, giving the Biancocelesti their first win in four Serie A games.
Despite their inconsistent start to the campaign, Petkovic insists he would not have faced the prospect of the axe had Klose not found a way to break Cagliari's resistance at the weekend.
"If we had lost today, we would have done anything but talk," he told Sky Sports Italia. "Instead we won. There is some positivity now, but we’re aware of the pressure coming from the outside.
"[Klose] is a very important player. He is one of the leaders of the team, and I am very pleased that he has been proven his strong character with all this criticism raining down on him.
"Did it save my job? I had no signs from the club suggesting I would be in trouble if we failed to win.
"We were relaxed in the second half, believed in what we had to do and in the end achieved it.
"It was important to score. We faced a team that knows how to play and be aggressive. We heard the jeers when we started to make some mistakes and felt the pressure psychologically, but I must compliment the lads for keeping calm till the very end.
"Just so to clarify, we can only be strong if we are united. [The anger of the fans] is a little our fault. We dropped three or four points, but I've never seen a team that did not want to give more, unless they possibly could not.
"The boys are healthy and clean, and they want to fight for the jersey."
Petkovic is refusing to make any excuses for their sluggish start to 213-14, but is hoping to get injured players Andre Dias, Giuseppe Biava, Abdoulay Konko, Senad Lulic and Emiliano Alfaro back in contention as they begin a tough run of fixtures with a trip to AC Milan on Wednesday.
"We must get our injured players back," he continued. "For two and a half months we have not had the full team and, since last year, six to seven players are missing, something that has not happened to the other teams in the league. But I have never sought excuses, I believe in the team I have."