Joachim Low's men went into the game knowing that they needed to win to have any hope of staying in the World Cup.
Sweden, however, took a first-half lead through Ola Toivonen, with Boateng slow to react to the striker's movement.
"Boateng's walking around the place like he's playing Sunday League football," Keane said. "He's been a disgrace. Get him off."
Neville added: "Roy is absolutely right. The [Germany] centre-backs have been a joke.
"I mean Boateng, for some reason, seems to think he is [Franz] Beckenbauer, thinks he's the player. He's played under Pep (Guardiola) and started to believe he is a fantastic football player.
"He has been a joke in this first half. He's got delusions, thinks he is a player; he's wandering forward, ambling in the game."
Keane got his wish in the second half, with Boateng sent off in the closing stages.
However, with Marco Reus having equalised, the reigning world champions snatched victory in the 95th minute through Toni Kroos' brilliant free-kick.
"Germany played better with out him," Keane added after the game.
Germany face South Korea next, with their progression still not certain.