Kai Havertz headed in Joshua Kimmich's free kick to give four-times world champions Germany a second-minute lead, but World Cup co-hosts United States snatched a stunning equaliser through Antonee Robinson.
Leroy Sane then scored in the 57th minute to seal Germany's victory at Soldier Field in Chicago.
"Overall, I think it was a good performance. I am happy with the performance of everyone. We play one of the most important teams in the world," Pochettino told reporters.
"I think we need to be happy with that. We compete, (we were) unlucky, I think it was as an even game... It was an amazing challenge for us to see how we react, how we show character, how we show togetherness, how we start to play under pressure."
The U.S. open their Group D campaign against Paraguay on June 12 at SoFi Stadium near Los Angeles.
"We were demanding a lot to the player(s) in the last two weeks. I've seen (us) overload the player(s) and the team," the Argentine manager said.
"Now (we have) to assess the load and be intelligent in the way that we are going to arrive to the Paraguay (game), in the best condition, fresh with energy."