Mark O'Hara hit the post for Kilmarnock in the first half
Kilmarnock hit the woodwork three times at Balmoor Stadium and lost the bonus-point shootout to Peterhead after a goalless draw, but progress in the Premier Sports Cup as Group H winners.
Neil McCann's side have scored just twice in four games although they kept clean sheets in all of them to finish on nine points, one ahead of Hamilton Academical.
The top-flight visitors were on top throughout and teenage defender Euan Bowie, making his first start, was denied by a good save from Jack Newman.
Mark O'Hara was the first Kilmarnock player to hit the frame of the goal when he dinked a cross from Michael Schjonning-Larsen against the post.
Joe Hugill and Greg Kiltie went close early in the second half before Tom Lowery hits the post with curling shot and Tyreece John-Jules headed the rebound wide.
There was a scare for the Ayrshire side when Cammy Smith shot into the side-netting from a Peterhead break.
John-Jules hits bar with a header but a point was enough for Kilmarnock, making the penalty kicks moot as Roshaun Mathurin was the only player to miss from the spot.
