Phillips missed a penalty and a string of good chances in the weekend 0-0 draw with Chelsea, but Kilbane insists the goal burden must be distributed more evenly.
"We are hoping Kevin gets all our chances and that is the way it is turning out for us. But we can not continue to rely on Kevin the way we do," said the Irish winger.
"If he doesn't tuck the chances away, we haven't got the goals from the rest of the park to kill teams off.
"So this is something we must improve on. Some of us have to get three or four goals a season."
Seven of The Black Cats' 13 league goals this season - only Leicester and Derby have scored less - have been scored by Phillips highlighting his importance to Peter Reid's men.
