In the summer of 2012, Klinsmann watched his USA side beat Scotland 5-1 in Florida when they were under the guidance of Craig Levein.
However, the former Germany striker believes Scotland have made the right decision in appointing Strachan and insists they are on the way up.
Neither side showed enough creativity to snatch the tie in Glasgow with Aron Johannsson's late strike one of few chances for the USA to clinch victory.
Scotland are now unbeaten in three and Klinsmann - who was on the losing side when the managers met as players at White Hart Lane as Strachan's Coventry beat Tottenham - believes the Scotsman has what it takes to lead the national side.
"It was clear to see that Scotland are on the way up," the former Germany manager said.
"Tonight confirmed that, they showed that they could beat you at any moment.
"There was no comparison between this game and the last game but we knew that would be the case.
"They are a different side, they are compact, focused and serious.
"They have got the message from Gordon, they are building towards the 2016 qualifiers and you could sense that tonight."
Klinsmann's USA will remain in Europe to face Austria in another international friendly on Tuesday evening.