Hamann had earlier fired shots at Kane while questioning his ability to influence matches on the biggest stages.
“He wasn't brought in to score a hat trick against Darmstadt,” Hamann wrote while criticising his failure to find the net against Bayer Leverkusen, Aston Villa, and the Champions League quarter-final against Real Madrid last season.
“He hasn't done that yet. I remain sceptical about the star striker.”
Kane's performance against PSG did not help his cause and Hamann did not let go of the opportunity to have a go at him again.
Speaking on talkSPORT Breakfast, Hamann said: "I went to the game yesterday and I’ve got to say he was very poor, I don’t think he had a shot on target and he pretty much played the same way yesterday as he did at the Euros for England. I think the jury is still out on whether he’s got it against the best teams - because he didn’t do it for England.
"I watched him against Ireland last week and he was poor. He played a wonder ball for the penalty but honestly, that’s not enough for an England captain. The World Cup is about 18, 19, 20 months away. Will he be the player or the captain to lead the line for England?”