The Red Devils slipped to fifth on the table, with fourth-placed Arsenal having three games in hand, after the defeat at the Etihad Stadium.
Jadon Sancho's equaliser after Kevin De Bruyne had given the hosts the lead only proved to be a consolation as Pep Guardiola's side scored three more to record a resounding victory.
Keane was unimpressed particularly with United's second half output as City assumed complete control and coaxed to victory.
Keane said on Sky Sports: "They did give up, and for a player in any game to give up, it's unforgivable really.
"The beauty of top-level sport is there's no hiding place. I know United have done well here the last couple of years. We saw all the United shortcomings today.
"There's ways to lose football matches. We've all lost football matches. But the way United lost it today, they stopped running, they gave up. There are players not running back, that's what I don't understand."
"The manager will be criticised, and the tactics," said Keane. "But players not running back when you're playing for Man United, it's really unacceptable, it really is. They threw the towel in, which is shameful.
"It's hard when you're out there and you're up against a really good team and they're keeping the ball and you can't get it back, but I go back to it, we see some of the goals and you've got to run back, you've got to tackle.
"United players have shown quality over the years but we've just seen a reflection of where the team is and where the club is. It's just so far behind the other teams."
Keane added: "Whatever's gone in the dressing room, and we hear noises all the time, and we hear about problems obviously with the new manager maybe coming in, and recruitment."
"But your own bit of pride eventually has to kick in at some stage. There were five or six players who should never play for Manchester United again. Just shameful, shameful that you can't run back and put your body on the line.
"I thought City had a couple of gears to go. They toyed with them. They [United] gave up, and shame on them."
