Jones was dismissed just before half-time during Saturday's 2-2 draw at the Stadium of Light after primarily pushing Ilunga in the chest.
The Hammers full-back fell to the ground clutching his face and Black Cats striker Jones was promptly shown the red card by referee Andre Marriner.
Black Cats boss Steve Bruce has confirmed he will punish Jones for the dismissal, but expressed his disappointment at Ilunga's reaction.
It is a view shared by his skipper Cana, who believes Sunderland need to learn from such situations in the future.
"He didn't really want to hurt him, he just pushed him a little bit," said Cana.
"It was the reaction of the opponent which got him the red card. It should have been a booking, but he made a lot of cinema out of it.
"We must learn to be a little bit more experienced in these situations."