Klinsmann's men twice led before going down courtesy of a Nicklas Bendtner hat-trick in Aarhus on Wednesday.
That meant a fourth defeat in five outings for the USA, who are making squandering leads an unwelcome habit, having also held second-half advantages during recent friendly reverses to Colombia and Chile.
Klinsmann is keen to highlight the positives of a team in transition post-World Cup, but he concedes that losing in such a manner, even against esteemed opponents, has been tough to take.
"Right now we are choosing highly competitive opponents like Denmark, Switzerland, Holland and Germany in order to help evaluate new guys and new combinations," he told US Soccer's official website.
"We know it's a difficult approach that we have taken. In this period, we want to learn. We want to see things about our players; how they react under pressure, play against excellent individual talent, communicate and fit in with the team.
"This causes us to swallow some bitter pills from time to time."
The former Germany and Bayern Munich boss expects no let-up against a talented Swiss outfit on Tuesday, particularly as the US will once again be without talisman Clint Dempsey due to a hamstring strain.
"Switzerland is a great team," Klinsmann added. "From a style perspective, it's a little bit similar to Denmark.
"They move a lot off the ball, they're very technical and they have a couple of special individual players like Xherdan Shaqiri from Inter who can turn it on in a second and make a difference.
"So you've got to be focused, alert, concentrated and aggressive for all 90 minutes. That's what we're trying to do."
Switzerland, who secured a top seeding for the World Cup in Brazil last year, beat Estonia 3-0 in their latest Euro 2016 qualifier on Friday night.
Fabian Schar, Granit Xhaka and Haris Seferovic were on target as Vladimir Petkovic's team continued to repair the damage caused by a nightmare start to the campaign, as they suffered back-to-back losses against England and Slovenia.
Petkovic pinpointed Shaqiri as being pivotal to the victory and believes the attacker's January switch from the Bayern Munich bench to regular first-team action at Inter will reap continued benefits for the national side.
"The first half [performance] was pretty good, we pressed well," he told reporters.
"Shaqiri is a very important player for us and a big talent. Since he joined Inter he has played regularly and now he has more flow to his game."
