The USA looked set to secure a round of 16 berth on Sunday when they led 2-1 in second-half stoppage time against Portugal but Silvestre Varela's very late header saw the match finish 2-2.
The result means both Germany and the USA are on four points ahead of their clash on Thursday, while Portugal and Ghana have a point each.
Germany and the USA could ensure they both advance with a draw, prompting questions at Klinsmann's post-match press conference in Manaus that he would approach compatriot and the German's coach Joachim Low to organise the result.
Low was Klinsmann's assistant when the latter led Germany to the semi-finals of the 2006 World Cup in front of their home fans.
But Klinsmann rejected the idea of collusion completely, claiming it is against the Americans' nature.
"The US is known to give all they have in every single game, otherwise Mexico wouldn't be here," he said.
In their final game of CONCACAF World Cup qualifying last year, the USA had already booked their ticket to Brazil when they travelled to Panama and trailed 2-1 late in the match.
That result could have seen the Panamanians advance ahead of the Americans' arch-rivals Mexico.
Instead, Graham Zusi and Aron Johannsson both scored in additional time for the USA to secure a 3-2 victory, ending Panama's hopes and saving Mexico.
While it was Klinsmann's men who let in a late goal at the Arena Amazonia on Sunday, the 49-year-old coach did not hold back in praising his players.
"All of them fantastic," Klinsmann told ESPN.
"They absolutely went to their limits but this is what it is now. In games like that, you have to prove your point and show your quality. You want to show the world that you're the best soccer players in the country.
"And that's what they're doing right now. They did an amazing job. We were that close. So we didn't make it quite yet. We have to make it against Germany."
Klinsmann also took a shot at FIFA, claiming their scheduling of the group phase has given the world's traditional top teams an advantage in Brazil.
"We have one day less to recover. They (Germany) played yesterday, we played today. We played in the Amazon and they played in the very kind of location where they don't have to travel much," the former German striker said.
"Everything was done for the big favorites to go and move on. We have to do it the tough way but we're going to do it the tough way."