Johnston was in the starting line-up while Stockdale was on the bench in Korea's second city, Busan.
South Korea stunned Scotland by taking the lead early in the first half as the Scots struggled in the muggy conditions. By the time Stockdale took the field in the 63rd minute Scotland were 2-0 down and it was 3-0 just minutes later.
Alan Johnston was replaced before Scotland grabbed a consolation and the South Korean's wrapped up a 4-1 victory in the dying minutes.
Both players will be hoping that Scotland fare better next week in Hong Kong when they play in a mini tournament against Hong Kong and South Africa.