Klinsmann, who has come under pressure in the past year after a series of setbacks, said the players never recovered their composure after suffering the hammer blow of an Argentina goal in the third minute.
The German World Cup-winner said his side had showed the Argentines too much respect over the remainder of a contest in which they managed zero shots on or off target.
"I think you could clearly see when we went 1-0 down, we had far too much respect and they were able to play their game," Klinsmann said.
Klinsmann cited the example of Lionel Messi's magnificent free-kick, which put the Argentinians 2-0 up midway through the first half.
Also Read
The US coach said his team had failed to spot Argentina's players moving the position of the dead ball into shooting range.
"I think in general we had too much respect and that shows in little incidents," he said.
"The free-kick from Messi they pushed five yards up one step at a time," he added. "I was screaming at the referee and the fourth official and that's why he's suddenly in range for shooting that goal."
Those are little things that we have to try and figure out. We're just too nice, too nice in those moments."
Still, Klinsmann insisted there was no shame in losing to an Argentina team he regards as the world's best side.
"You saw tonight why they are the number one team in the world," he said.
"You have to give a huge compliment to Messi, (Gonzalo) Higuain and (Javier) Mascherano and all these guys."
"I told the guys there's nothing to be ashamed of," he added.
"We have to learn and move forward. There will always be a step backwards and then two more steps forward. That's part of the process. We have to keep our heads up and swallow it. But Argentina are a special team."