Jones was dismissed in the 45th minute of a stormy clash at the Stadium of Light following a push on Hammers defender Herita Ilunga which has sparked off a war or words between the two clubs.
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Black Cats boss Steve Bruce was annoyed by Ilunga's reaction as he went down holding his face when Jones pushed him in the chest.
However, Jones has not escaped the wrath of Bruce as he will now serve a three-match ban.
"That's the disappointing thing of the sending-off, not just dealing with West Ham last week, we have got to go into the next three games without Kenwyne," explained Bruce.
"That's why he has been punished. The club has punished him.
"We have got a standard disciplinary procedure which comes into effect. It's quite simple, it's there in black and white for them.
"Kieran Richardson was exactly the same two weeks ago. If you get sent off for two yellow cards or mistimed tackles, that happens, or you are the last man and you may get handballed or something, that happens.
"But something silly - we have all done it, we have all been there, the heat of the moment and you react.
"He will be a miss because the strike-force for me has been the reason why we are going the way we are at the moment, because we are a threat at the top end of the pitch.
"Being without Kenwyne, we will have to adapt."