Uruguay coach Oscar Tabarez admitted he warned his side about the potential of a World Cup upset against Costa Rica.
Despite taking a first-half lead through Edinson Cavani's penalty, Uruguay conceded twice in eight minutes to Arsenal's 21-year-old midfielder Joel Campbell and Oscar Duarte's first international goal.
Substitute Marcos Urena added a late third before frustration got the better of Maxi Pereira, who was sent off in added time for a wild hack at Campbell.
"This can happen to any team, we had talked about this topic after what happened to Spain (who lost 5-1 to Holland)," Tabarez told his post-match press conference.
"Neither team can believe that there are things that cannot happen.
"I don't know what Costa Rica's limit is but today they played well.
"They were tactically better than us, which reflects well on their coach and players.
"When they took the lead, they gave us space and let us play where we couldn't do them any harm.
"Now we're going to try and get back on track against England."
Uruguay's all-time leading scorer Luis Suarez spent the whole game on the bench as he continues his recuperation from keyhole knee surgery last month.
Tabarez admitted there was no guarantee the Liverpool forward would return against England on Thursday in Sao Paulo.
"Luis Suarez is no longer injured, because he wouldn't have been a substitute if he was," he added.
"He has gone through the phases that we have foreseen in his recovery and we will have to see if he can find fitness.
"As we said from the beginning, if he meets the challenges, we will see how he can get into the team - and at which point.
"For us, he is a key player. He has great potential and has a lot to contribute to the team.
"We need him to reach a point where he can play in a match. It was he who demanded to be on the bench, not watching from the stands. It would have been very difficult for him to play though.
"He was a serious doubt, you need to have a certain fitness level - you need to be able to reach the highest standard.
"There were certain concerns over his fitness and it was very improbable that he would play. We will see about England."
Costa Rica coach Jorge Pinto was delighted with the composure shown by his players.
"It's a historic victory to have won against a great team, a tough team that is not easy to beat," he said.
"We are happy and I want to congratulate the team for the attitude they showed.
"The players kept their heads after Uruguay scored. They were composed, stuck to their game and played with a lot of heart.
"It's an important win for us and it gives us hope, though we haven't won anything yet."