The veteran forward made history with the Biancocelesti but believes his team-mates are equally deserving of praise
The Germany international scored all of his goals in an incredible 40-minute spell in the routing of the Rossoblu, making him the first Lazio player ever to achieve the feat and the first person to score five in a single league game since Roberto Pruzzo in 1986.
However, while Klose admitted he was "pleased" with the achievement, he opted to share the plaudits with his team-mates and the club who consequently picked up their first victory since March.
Speaking to reporters, Klose said: "Have I ever scored five in one match? I did it once when I was with Kaiserslautern, but today my five goals were all about the team as a whole," he told reporters.
"I'm pleased with my goals but I'm very pleased with the team performance. We worked very hard today and we were in the middle of a rough patch and we reacted well. I'm happy the team has returned to winning ways.
"I dedicate all five goals to my family and to Lazio, who are now my second family."
Lazio climb to seventh in the Serie A standings and resume their push for a Europa League place with a visit to Inter on Wednesday.