The striker was on target in stoppages to beat arch-rivals AS Roma 2-1, ending a run of five consecutive Derby della Capitale defeats.
"You have to believe right to the end, as it's always possible to score a goal," said Klose in his Press conference.
"I am a striker, so making the team win is my job. The important thing is never to give in, as that is the great thing about football.
"I had a T-Shirt under my jersey ready to show if I scored, but didn't have time to get it out! I have a good rapport with the fans and I don't know if it'll change after this derby, but they have always shown me great affection."