City featured a youthful line-up on the day, but still completely outclassed Exeter.
Caldwell said afterwards: "I think we started the game quite well. We had a moment from a corner, the goalkeeper made a good save. We had other counter attacks where decision making could have been better.
"I think the goals we conceded were poor. At any level you play at you can't concede goals like that."
7,800 Exeter fans made it to the Etihad and stayed until after the final whistle.
Added Caldwell, "Remarkable. I heard them when Joe and the goalkeepers, when the team came out for the warmups. They stayed with us and clapped us at the end when it was a really humbling defeat."
Meanwhile, veteran striker Josh Magennis conceded: "I think just coming away from the game, we just didn't realise just how relentless they were."
"Obviously you can see it on the television, but when it comes to playing them and getting up-close and personal, they were very efficient in how they played today and they didn't miss any of their chances."
The Grecians had some early chances and were denied by City goalkeeper James Trafford.
However, a realistic Magennis joked: "Maybe the game would have ended differently in those chances had gone in, but if I had wheels I would have been a bike!"