Making their maiden appearance as an independent nation, Serbia delighted their fans in Auckland's North Harbour Stadium and thousands back home after Nemanja Maksimovic scored a late extra-time winner.
"They can get to the top of the world and I can tell you that there are a lot of good players in this generation who will play in the best games in the world over the next 10 years," Paunovic told Serbia's B92 website (www.b92.net).
"This is the time for this generation to grow up and say farewell to youth football and this is the best way to do it.
"It is a massive achievement but the essence is how we did it. Not the kind of football where you dominate all the time, but we defended as if our nation's fate was on the line."
Having lost their opening group match to Uruguay 1-0, Serbia advanced into the last 16 with 2-0 wins over Mali and Mexico.
They needed either extra time or penalties to win each of their four knockout round games and showed steely determination in the final against a more talented Brazilian outfit who were strong favourites to win their sixth title.
Serbia's feat emulated the former Yugoslavia's 1987 triumph and goalkeeper Predrag Rajkovic revealed they drew inspiration from watching footage of a side featuring the likes of Zvonimir Boban, Davor Suker and Predrag Mijatovic.
"The 1987 side were exceptional and I think we've proved that we're just as extraordinary," Rajkovic, who was named the best goalkeeper of the tournament, told FIFA's website (www.fifa.com).
"We are one team with one heart and that's been our motto from the start. We've all really enjoyed this adventure and the experiences we've had here in New Zealand."
Having also won the Under-19 European Championship in 2013, Serbia's superb results at youth level are in stark contrast to the senior team's poor performances in the last five years.
After exiting at the group stage of the 2010 World Cup, Serbia failed to reach either Euro 2012 or the 2014 World Cup and have only a slim chance of qualifying for next year's European Championship in France.
"These young lads have set an example to all our national teams how proudly they should don their Serbia shirts," former Yugoslavia and Aston Villa striker Savo Milosevic told Belgrade daily Sportski Zurnal.
"It is now up to us to nurture the values they displayed," added Milosevic, now the Serbian Football Association vice-president.
(Writing by Zoran Milosavljevic; Editing by Toby Davis)
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