Toni Kroos' 95th-minute winner spared the defending champion's blushes against a spirited Swedish side but for most of the game, Germany looked in big trouble.
Boateng was one of many who struggled with his culminating in a red card in the second half after two bookable offences.
Before he was sent for an early bath though, the centre-back was on the receiving end of a scathing attack by the two former Manchester United players.
Keane begam by saying: "The two centre-halves will give you a heart-attack. Boateng has to come off, [he's] been a disgrace.
"He's been walking around like it's a game of Sunday league football. He's been a disgrace, get him off".
Neville agreed: "Roy is absolutely right, the centre-backs have been a joke, an absolute joke.
"Boateng thinks for some reason he is [Franz] Beckenauer, thinks he's a player. He's played under Pep [Guardiola] and started to believe he's a fantastic footballer.
"He has been a joke in this first half. He's got delusions, thinks he's a player; he's wandering forward, ambling in the game.