Nam Tae-hee's first-half header decided the contest in Canberra, and Australia's subsequent 4-0 thrashing of Oman means Stielike's side are assured of a place in the quarter-finals.
Despite the victory and progress to the last eight, Stielike was less than satisfied with his team's performance.
"Kuwait were much more aggressive than I expected," he said. "They were a different team.
"We talked a lot and prepared about this match, but they were superior than us most of the time in the match.
"I really don't want to admit it but they were better at passing and duels. We were really lucky to win."
South Korea's squad has been heavily affected by a raft of injuries and illness, with Lee Chung-yong's tournament over after he sustained a hairline fracture to his right tibia.
"Lee Chung-yong left the team and went back to Korea due to injury," Stielike said.
"Kim Chang-soo has not recovered yet. We registered 18 players for this match and only 14 could actually play. I didn't expect us to struggle this much. It was really a difficult match.
"Lee Chung-yong, who would start every match, has vast experience. But we have to face the situation. These things always happen in football.
"Son Heung-min has been sick in the past two days. He was better yesterday but he had to go to hospital today. We have to do our best to maintain good condition."
South Korea face Australia on Saturday, with top spot in Group A up for grabs.
