Tabarez admits good fortune
South Korea hit the post with a Park Cho-Young free-kick early on, but Uruguay were soon ahead through Luis Suarez after some poor defending.
Lee Chung-Yong then scored a deserved equaliser as South Korea dominated the second half, but that sparked a reaction that led to a stunning 80th-minute winner from Suarez.
"It was a difficult game to play and I think our win means more because of this," Tabarez said. "We were surprised by their play. We wanted to finish the game in the second half. Their goal was key to our win because we improved after that. We showed class in the final minutes and Suarez scored two spectacular goals for us."
He added: "They played a great game. Maybe luck helped us, but this is football. This confirms that football around the world is getting better and how Korea are always improving. They are perhaps the best team in Asia.
"It was a tough game for us and a really big win. I am really happy and happy for the fans back home. Now we have to prepare for the future and see who we play out of USA or Ghana."
Suarez said he feared South Korea would win the game after their equaliser but believes they eased up after scoring.
"I cannot explain my happiness," he said. "I have always dreamed about this moment. Obviously you always want things to go well and to go far in the World Cup and we are happy.
"At 1-1, we were scared, they played well, but then they stepped off the gas and we became strong. I couldn't believe the second goal. All I want now is to celebrate. I dedicate this win to all the fans and my family."