The Spanish are level with Croatia on four points at the top of Group C ahead of their clash in Gdansk on Monday and Torres said Russia's 1-0 loss to the Greeks showed even teams with one foot in the last eight needed to be on their guard.
Italy, who play eliminated Ireland, are third in Group C on two points and would be knocked out if Spain and Croatia play out a scoring draw of two goals each or more.
"The result Russia had yesterday is a good wake-up call for us and all the teams that we need to win the last group game," Torres told a news conference at the PGE Arena in the Polish port city.
"Even with six points [from your opening two games] you can go out," added the 28-year-old, who netted twice in Spain's 4-0 drubbing of Ireland on Thursday.
"Croatia need to win as well and we have watched videos of them and are aware of their strengths and know how to approach the game," he said.
"We believe we can play our football and win the game but it's important to respect the opponent."
Spain coach Vicente del Bosque told a later news conference Russia's fate was the latest example of a shock result in a sport that regularly threw up surprises.
"It tells me that in football there are always lessons like this," he said, citing the semi-finals of this season's European Champions League, when Chelsea stunned Barcelona and Bayern Munich knocked out Real Madrid.
"That's football and we always have that in mind and have our five senses primed," Del Bosque said.
