A handball on the goal-line by Luis Suarez prevented Ghana'sDominic Adiyiah from scoring in the last minute and Asamoah Gyan missed the penalty - with Uruguay triumphing in the shoot-out that followed.
The South Americans' goalkeeper Fernando Muslera was the hero, saving twice from John Mensah, the Sunderland centre-back, and Adiyiah, in the shoot-out. Sulley Muntari, almost sent home earlier on in the tournament after a bust-up with Ghana's Serbian coach Milovan Rajevac, had given his side the lead before Diego Forlan equalised with a viciously-swerving free-kick for his third goal of the finals.
Tabarez claimed the Ajax striker, who was subsequently sent off, had reacted instinctively. He said: "When there is a handball in the penalty area there is a red card and the player is thrown out of the game. Saying we cheated Ghana is too harsh a word to use. We also abide by what the referee did. It could have been a mistake. Yes he stuck his hand out but it's not cheating. I don't think it's fair to say that.
"I think it was instinctive. The player instinctively reacted and was thrown out of the match and he can't play the next match. What else do you want? Is Suarez also to blame for Ghana missing the penalty? We try to be dignified and if we lose a match we look for the reasons for it. You shouldn't look to third parties. This is football. There are consequences to that handball and he didn't know that Ghana was going to miss that penalty."
For Uruguay it confirmed their first semi-final appearance for 40 years - they play Holland in Cape Town on Tuesday - and the result sparked joyous celebrations in the country.
Tabarez added: "I hope the party goes on for three or four days! I am the coach of the team, I'm a pro and even so I lack the necessary calm to carry out an objective analysis of what happened. We achieved our goal but we didn't play as we wanted to. Our rival was extremely tough. We were lucky. Luck is important and I really cannot say much more. Those who believe in fate or destiny they might be able to explain it. I don't believe in that."
Ghana coach Rajevac hailed his heroic Black Stars and blamed a "sporting injustice" for their agonising exit. Rajevac said: "There are no words to express what we feel. This is sport's injustice but I congratulate Uruguay - they were the lucky ones.
"We had an historic opportunity to reach the semi-final - we had a penalty but you saw it all. The opponents had the psychological advantage in the shoot-out. Everything happened so fast. We really had big support and it would have been a fairytale if it ended well for us, but I would like to congratulate Uruguay on reaching the semi-finals.
"I'm very proud. We managed to achieve a great result and the whole of Africa supported us. We didn't deserve to lose in such a way and it's difficult to talk about it at the moment. We had bad luck that's all I can say."