Jefferies targets 'a cup double'
A victory on Saturday could put the Ayrshire side nine points ahead of the bottom half of the SPL three games before the split.
And Jefferies feels that would give them a huge psychological boost ahead of the Hampden final against Hibernian the following weekend.
He said: "It would be massive, the pressure would be off.
"Our target this season was the top six and a decent cup run. The cup run is in the bag, we can't go any further than the final.
"We have not made the top six yet so that is the key. We want to be in the top six.
"I would say the cup final will act as a spur, I don't want them to think about the cup final other than that they are playing for their place.
"If they play for their place hopefully the spin-off will be a good performance on Saturday.
"We are in the driving seat, we think we can take a massive step to make it very difficult for the rest if we win on Saturday.
"So it's two cup finals on the trot."
Killie drew level on points with their cup final opponents last weekend when they won 2-0 at St Mirren.
Jefferies would take encouragement from lining up at Hampden above the Edinburgh side in the table.
Jefferies said: "We are level with Hibs, so they are in a chase for the top six as well. If we win and Falkirk do anything, we go above them.
"If we win, we go nine points in front with three games left so it will be strongly in our own hands.
"Football has a habit of kicking you in the teeth, but I think we would deserve it.
"We have been in the top half most of the season so for consistency levels nobody could deny us if we made the top six."
Killie edged a seven-goal thriller in their last game against Inverness 4-3 and Jefferies expects another close contest.
"We always have a tough game, very close games, there have been a lot of draws between us," the Rugby Park boss said.
"We had a cracking game against them the last time as well, 4-3.
"They've given themselves a chance to be in the top six with their last-minute win last week."