Altidore hurt his hamstring in the USA's 2-1 win over Ghana on Monday and appears likely to miss Sunday's Group G clash in Manaus.
Klinsmann revealed that he had urged his men to move on from their opening-game triumph at the FIFA World Cup, and believes they can overcome a Cristiano Ronaldo-led Portugal.
"We only talk now about how we can beat this Portuguese team with all these amazing players they have," the German said.
"This is our goal and we believe in it and believe we can go to Manaus and beat them. We want to get in the next round and if it takes beating Portugal then this is what we have to do."
Klinsmann was unwilling to say whether Altidore would miss the encounter as the 24-year-old awaits the result of scans.
He is keen to keep Portugal guessing, but admitted that the Sunderland foward's absence would be a blow.
"I don't want to go too deep into details because obviously we want Portugal to guess a little bit as well but when one of your key players is not available does it change certain things? Absolutely it does," Klinsmann said.
"Jozy is a very strong and key player in our group so we will think about the right way to handle the situation.
"We still can field 11 and we are not a man down, we have somebody coming in and we will make it very difficult for Portugal in Manaus and find solutions."
Klinsmann feels goal difference could be key after Germany thrashed Portugal 4-0 in their opening game, but he will not go into his team's second match looking for a draw.
"We have very good players in this squad and we have the confidence to go into that game and say, 'we are here and want to beat you and get into the next round'," Klinsmann said.
"Our approach is not to go to Manaus and defend for 1-1 or 0-0 or whatever it is, but we go there and want to win this game."
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