Low also revealed he told Gotze to show the world he was better than Lionel Messi minutes before the substitute came on to score the winner.
Victory gave Germany a fourth World Cup title and first for 24 years.
Gotze, 22, said: “It is an unbelievable feeling. You score that goal and you don’t really know what’s happening.”
Gotze, who began the 2014 Fifa World Cup in Germany’s starting line-up, came on as an 88th-minute substitute for Miroslav Klose in Sunday’s final.
With seven minutes of extra time remaining, the Bayern Munich midfielder volleyed home with his left foot after controlling Andre Schurrle’s left-wing cross on his chest.
“He is the wonder who can play in numerous positions, he is the decider who can come on and make a difference,” said Low. “That is what he did.”
Gotze, who joined Bayern in a £31.5m deal from Borussia Dortmund last summer, added: “It’s indescribable. The dream has become a reality. It is absolutely sensational.”
Despite being on the losing side in the final, Messi was named as the tournament’s best player.
Coach Alejandro Sabella said the award was “very deserved”, adding: “He played a great World Cup to get us where he did.”
Germany counterpart Low, meanwhile, said victory in Brazil was the result of a 10-year project.
Germany were knocked out at the group stage of Euro 2004 without winning a game but have since reached three semi-finals and two finals at five major championships.
Before Sunday they had not won a tournament since tasting success in the 1996 European Championships in England.
“We’ve made constant progress and believed in the project,” said the 54-year-old Low, who became coach in 2006 after stepping up from his role as assistant to Jurgen Klinsmann.
“If any group deserves it, it’s this team.”