Former AC Milan boss delighted with the way his side showed World Cup form to beat the tournament favourites and suppress Lionel Messi
The game ended 1-1, but a penalty miss by Carlos Tevez after extra time proved crucial as Uruguay won 5-4 in the shoot-out.
Tabarez believes his side found it tough against the likes of Lionel Messi, but hailed their determination to pull through.
"We are very happy. We knew the team was improving and we had to do well against a team with great history, great players and the fans behind it," he told the press, as reported by Marca.com.
"And, in the hardest moment, and when we needed it most, we showed the things we saw at the World Cup.
"Now the whole dressing room will celebrate, and after that we have the chance to go even further, but it will not be easy."
On keeping Messi quiet, Tabarez said: "Messi is a great player when it comes to individual play, but we planned the game very well. He played a good game, but we are happy as it is not easy when you play against players like these."
Uruguay take on Peru in the semi-final showdown on Tuesday night July 19 in La Plata.