Tottenham striker and main goal threat Kane failed to register a shot on target for the second time at Euro 2020, having also underwhelmed against Croatia.
“He doesn't look up to speed," Keane said on ITV. "He's on his heels all the time and if England really want to compete in this competition, you need your star men to perform.
"We've seen [Romelu] Lukaku turn up, [Kevin] De Bruyne, [Cristiano] Ronaldo, they need Kane at his best.
"I'm glad Gareth [Southgate] took him off - there's talk about him being undroppable, he's the main man, if he's not performing, get him off. Rashford gave them a little bit more energy, but still not enough."
“Before the competition, there was all the talk of him might be leaving Spurs and maybe he's been distracted by that because that can be an energy zapper," Keane went on.
"If you thinking you're moving clubs or if you're in talks with other clubs, that's not helpful."