Dempsey was due to start at the windswept Candlestick Park in San Francisco but pulled out 10 minutes before kick-off due to a niggling groin problem.
The Seattle Sounders man aggravated the issue on Monday and felt it was not worth risking in a friendly - a view Klinsmann shared.
"No it's not serious at all," Klinsmann said.
"He had a little bit of pain yesterday already in training and he told me about it.
"And then in (the) warm-up, he was just a little bit nervous about it."
Dempsey also said he will be in action when Turkey visit the Red Bull Arena on Sunday.
He told the official MLS website: "Yeah, I'll be ready. (It's) just tightness.
"I was just feeling it a little bit (on Monday) and it was still tight again today, so it didn't make sense to push it in the game."
Goals in the last 15 minutes from substitutes Mikkel Diskerud and Aron Johannsson gave the US their win and although it was scrappy, Klinsmann remained upbeat.
"We're not concerned at all," the German added.
"We knew it was going to be tricky with the conditions out there. You need to keep the ball on the ground, even then if you hit a high ball, that ball is gone, it goes all over the place.
"I have to excuse certain elements because of the conditions. You can't play that one (and) two-touch game easily and play through it because the ball takes a different pace. It gets very difficult."
The United States will play Ghana, Portugal and Germany in Group G at this year's FIFA World Cup in Brazil.
