While Uruguay won their pool thanks to an impressive 1-0 victory over reigning champions Chile, Peru stumbled into the knock-out stages after going into meltdown in their final group match.
Uruguay are heavily fancied to progress when the sides meet in Salvador on Saturday.
"What happened to them against Brazil was a football accident, that doesn't happen very often," said Tabarez, 72. "Tomorrow, Peru have a chance and if we were in that situation we'd cling onto it tooth and nail. That's why we're expecting a very difficult match. When something like this happens, that's when self-love awakens within a group and a coach discovers a different team that looks to pick itself up."
Tabarez pointed to Argentina's rapidly changing fortunes as evidence of how fickle form can be.
Argentina were bottom of their pool after two matches but earlier on Friday beat Venezuela 2-0 to qualify for the semi-finals.
"As I said the other day: who dares to discount Argentina? And no-one said anything. Now the same thing is happening with Peru," said Tabarez.
"It's on the pitch that the true history is written and there will be a rival fighting the same way we will be."
Peru coach Ricardo Gareca admitted he looks up to Tabarez, the senior figure amongst the tournament's coaches.
Tabarez is "a wise man and an example for all us coaches," said Gareca.
Peru began their campaign with a draw against Venezuela and then beat Bolivia but they were at sixes and sevens in the defeat to Brazil.
"We need to be more consistent and that's the way to win. It's the only way. Hopefully we'll play well and achieve that stability we need," said Gareca.
"The most important thing is to put behind us what happened (against Brazil), we achieved our aim of qualifying (although) not in the way we wanted."