Joachim Low's men capped a brilliant Brazil campaign with a 1-0 extra-time victory over Argentina in Sunday's final courtesy of Mario Gotze's volley.
Klose broke the record for World Cup goals - 16 - during the tournament, and the 36-year-old Lazio forward said he will reveal whether Germany's fourth World Cup victory will mark his final international.
Klose has 137 caps for Germany, and 71 goals in national colours.
"It is outstanding. This crowns everything. We were second once, third twice - it is world class, I still cannot comprehend it," Klose said, as reported by DFB.de.
"The team performance was important, we wanted to stay calm also because we knew that we have the better quality.
"I do not know yet if I go on for the national team. I'll have a couple of nights to sleep on it and then make the right decision."
Klose also claimed credit for inspiring Gotze, as he was substituted off the pitch for the man who scored the match-winning goal.
"Before Mario came in to play for me, I told him: 'You can make it happen'," Klose said.
Midfielder Bastian Schweinsteiger said the effort of Low's group was extraordinary, and he made special mention of the squad members who were on the bench in Rio de Janeiro.
"We enjoy the moment, incredible. Thanks to all of Germany for support. We have felt that here, as you stood behind us. Today is celebrated everywhere, we give full throttle here," the Bayern Munich man said.
"Incredible performance, but as the guys have called off the bench, I have never experienced something like that. This gives so much power, the only reason why we won the cup."
