The ex-Bayern Munich man feels the attacking midfielder has been underwhelming in recent years, while Christoph Metzelder claims he "takes it easy" too often
The 22-year-old joined Bayern from Borussia Dortmund in the summer of 2013, but failed to live up to the high expectations in his first season at the Bundesliga champions as he struggled for form and fitness.
Hamann has been less than impressed with Gotze's performances for Bayern so far and feels the creative forward is already behind in his development.
"With the talent he has, Gotze should already have been at a different stage of his career," Hamann told Sky.
"Gotze has to get going now. He has six or 12 more months to make that step up.
"You cannot just put in some half-hearted effort now and say that will you will give it your all next year. It doesn't work that way."
Former Dortmund defender Christoph Metzelder, meanwhile, was equally critical of Germany's World Cup hero and has urged him to put in more hard work.
"Mario takes it easy a lot of times and often relies too much on his talent," he added.
Gotze netted 10 goals in 27 Bundesliga appearances in 2013-14 and went on to score the crucial extra-time winner against Argentina in the World Cup final.