The north London club signed Maddison from Leicester in the summer and he has been pivotal to their good start to the season.
Maddison has two goals and has provided four assists in his first six Premier League games for Tottenham and has been the creative hub of the team.
Carragher also feels Tottenham emerged as the perfect club for Maddison as they needed a creative spark like him to carry them after Harry Kane left for Bayern Munich in the summer.
The former defender also stressed that Postecoglou deserves a good amount of credit for devising a way to get the best out of the player in a system that exploits the midfielder’s creativity.
He admitted that Maddison has quickly emerged as the symbol of a new bold era at Tottenham.
Carragher wrote in his column for the Daily Telegraph: “In a period of transition at a club in dire need of a spark after the sale of Kane, Spurs emerged as the perfect club at the right time under the ideal manager.
“Credit must be given to Ange Postecoglou for identifying how to maximise Maddison’s assets, encouraging him to sprinkle the creative dust while the coach gets a tune out of the players he has inherited.
“For now, seeing a team playing front-footed and imaginative football is enough for the Spurs fans, the team’s excellent start beyond their expectation at the start of a new era.
“Maddison has become a symbol of the fans’ growing sense that they ‘have their Spurs back’.”
Tottenham will depend on Maddison to provide the creative spark when they host Liverpool on Saturday.