Lukas Podolski marked his final appearance for Die Mannschaft with a stunning winner as Southgate’s new attack-minded formation built on a three-man backline was unable to conjure a goal in Dortmund.
England looked comfortable in possession and a far larger threat than the World Cup winners, only to be caught cold as Podolski’s 130th and final Germany appearance ended with a fairytale strike that secured victory.
“If you looking at chances we had the better chances in the game, as simple as that,” Cahill said.
“I think we will look back and reflect that if we take our chances we would have won that game.
“It’s a learning curve for us.”
Cahill, who was England captain on the night, said the terror attack on Westminster had been on the team’s mind before the match.
He added: “Obviously that’s terrible but we were focused on the job we had to do.”
Elsewhere, Scotland manager Gordon Strachan claimed their 1-1 draw against Canada was “invaluable” for his team selection ahead of Sunday’s crucial game against Slovenia.
Falkirk midfielder Fraser Aird capitalised on some slack defending to open the scoring for the visitors, ranked 117th in the world. Both sides had half-chances before Steven Naismith diverted home an equaliser.
“It was one of our better decisions to have a game,” Strachan said. “It has cleared up a lot of things, it has helped a lot of players, but it has helped the coaching staff in particular to where we are going on Sunday. We learned quite a few things.
“It’s not been a great night, it won’t be memorable in anyone’s minds at the end of careers but it was invaluable to me to use the information we collected for Sunday.”