Gotze came on as a second-half substitute before scoring with a volley in extra time as Germany beat Argentina 1-0 at the Maracana to win its fourth World Cup.
Low was seen speaking to Gotze during the break in extra time and revealed after the match that he told the Bayern Munich forward to show up Messi and make his country world champion.
"I told Mario Gotze to show to the world he is better than Messi and to decide the World Cup. That’s what I told him – I had a good feeling with him," Low said in his post-match news conference. "Gotze is a miracle boy. He can play in any position. I always know he can be decisive in a match and he scored a great decider today."
Low first joined the Germany setup as assistant to Jurgen Klinsmann in 2004 before taking over as coach after the 2006 World Cup on home soil.
The 54-year-old believes the World Cup triumph was the culmination of a decade of constant improvement and says Germany deserved to win a World Cup.
"We started this project 10 years ago and this is the result of many years of work, beginning with Jurgen Klinsmann," Low said. "Over these years, we made constant progress and improved performances until we did the ultimate thing we had to do.
"If there is one team that deserves this, it is these players. Guys like Per Mertesacker, Lukas Podolski, Bastian Schweinsteiger, Philipp Lahm, Miroslav Klose who have been in the group this whole time. The team spirit is unbelievable. They have unbelievable willpower and that is why we made it. The players gave everything, with Schweinsteiger leading them and Lahm running forever.
"I told them before the game that they would have to give more than ever before to do something they had never done before – win the World Cup. We are the first European team to win the World Cup in Latin America and this makes us proud. This deep joy and happiness will remain forever."