Two goals from star striker Luis Suarez, the second just 10 minutes from time, were enough to see off South Korea at the Nelson Mandela Bay Stadium in Port Elizabeth on Saturday and spark wild celebrations in Montevideo.
It is 60 years since Uruguay lifted the World Cup for the second time, and the odds on them doing so in South Africa remain long.
However, they have reached the last eight, where they will face the sole African survivors, Ghana, by conceding just one goal in their four games to date, and Tabarez wants his players to continue to enjoy the ride and not give up on anything.
He said: “Let’s see how far we can go on this stage. We are not building castles in the air, but I don’t see why we should be resigned to anything.
“We don’t have to renounce anything before playing the matches.”
Atletico Madrid striker Diego Forlan, however, has been in the game long enough to know tougher challenges lie ahead, and he is keeping his feet firmly on the ground.
He said: “It’s just one game, you know, an elimination game, and nowadays every team is going to be difficult, so we know it’s going to be tough.’’
Tabarez and his players swiftly turned their attention to Friday’s clash with Ghana, at Soccer City in Johannesburg, although the coach admitted he was having to pinch himself.
He said: “Before the game, I said to the players ‘if we accomplish our goal, we will have another week to enjoy ourselves’.
“We have to prepare for our upcoming match. I am very satisfied with my team. We don’t have to improve many things, simply capitalise on this and give our all against our next opponent.
“We are among the eight best teams at this World Cup. It’s true, but I still can’t believe it.”
URUGUAY: Muslera, Maxi Pereira, Lugano, Godin (Victorino 46), Fucile, Arevalo Rios, Perez, Pereira (Lodeiro 74), Forlan, Cavani, Suarez (Alvaro Fernandez 84).
SOUTH KOREA: Jung, Cha, Cho, Jung-Soo Lee, Young-Pyo Lee, Ki (Yeom 85), Jung-Woo Kim, Jae-Sung Kim (Dong-Gook Lee 60), Ji-Sung Park, Chung-Yong Lee, Chu-Young Park.
Referee: Wolfgang Stark (Germany).