The veteran striker, 36, made way for the Bayern Munich star after 88 minutes of play and head coach Joachim Low's decision eventually paid off in extra time when Gotze controlled a cross from Andre Schurrle before volleying home the only goal of the game.
|WORLD CUP SOCIAL HUB
|Keep up with all the latest news from Brazil and get involved in the debate on Twitter with our new World Cup Social Hub|
"It's outstanding, this crowns everything. We finished second once, were third twice, but this is world-class, I can hardly comprehend it.
"It was always a dream to once be up there getting the trophy and not just having to stand around and have to applaud others.
"The team's performances were important, we wanted to keep our calm because we knew we had the better quality to win it."
Klose became the all-time World Cup top scorer in Brazil following his goals against Ghana and Brazil to cap a superb international career, but the final against Argentina could very well have been his last game for the national team.
"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," the Lazio man added.