Lukas Podolski's thunderous strike secured the win for the home side at Signal Iduna Park in what was the 31-year-old's 130th and final match for his country.
Podolski's 69th-minute winner was Germany's first shot on target, with Adam Lallana having hit the post and Dele Alli missing a one-on-one during a first hour which England largely controlled.
And Cahill felt his side did enough to warrant a better result, telling ITV: "If you're looking at chances, we had the better ones, simple as that.
"I think we'll look back and reflect that, had we taken our chances, we win that game. It's a learning curve for us but if we're a little bit more clinical in front of goal...
"I thought we played well, especially first half, we controlled the game really well. But they took their chances."
Gareth Southgate used a 3-4-3 system in his first match since taking charge on a permanent basis, and Cahill felt there were encouraging defensive signs from the performance despite their lack of practice using the new formation.
"We've go into that formation for the first time," he added. "We've gone in off the back of the lads playing Saturday, Sunday, we've had a cool down and then one day where everyone's been out on the training pitch. It's difficult to play in a new formation and have everyone grasp it straight away.
"But there's a lot of positives from that."