The 24-year-old was involved in an extraordinary flashpoint in the closing stages of extra-time in Sunday’s game against Chelsea at Wembley , when he appeared to publicly undermine his boss Maurizio Sarri.
The Spaniard had gone down with an apparent injury and signalled over to the bench for treatment. With a penalty shootout looming, Sarri decided to replace Kepa with substitute goalkeeper Willy Caballero.
The incident will once again place Sarri’s position under further scrutiny, with his future already in doubt going into this game.
However, former Chelsea striker Sutton believes it is Kepa, who cost £71.6 million ($93.5m) from Athletic Bilbao last summer, who should leave the club and not Sarri.
“Kepa should never play for Chelsea again. That should be his last performance in a Chelsea shirt. He's a disgrace. I've never seen anything like it,” Sutton told BBC Sport.
“If I was Sarri I would walk. You cannot be undermined. Why weren't the players dragging Kepa off anyway?
“Kepa should be sacked, not Sarri.
“I still cannot believe what I have just seen. How can Kepa play for Chelsea again? How can he play for Sarri again? Something has to give. He has to go.
“I feel for Sarri today, he was under pressure anyway. How's he going to get through this?
It's mutiny at Chelsea. How do we see this situation panning out? Kepa has to go or Sarri has to go and I suspect Sarri will walk.
“He's been undermined - it's the worst thing that can happen to a manager.”
Kepa recovered to save Leroy Sane’s spot-kick in the shootout, though he failed to save another as City won 4-3 to win the trophy for the sixth time in their history.