The Dutchman experienced his first defeat as manager of the Merseyside outfit as they were beaten 2-0 by the Canaries in the third round of the competition.
After the match, Koeman told Sky Sports News: "That's football. I can't criticise the players, we worked hard tonight, the difference was that [Norwich] were very clinical.
"We had enough chances to score and we didn't - that's the difference. It's disappointing because in the Cup you don't get a second chance. We were not clinical enough, we did not score, but we played well, with a lot of composures. It's all about scoring goals and that was not today."
The result ends a six-game unbeaten run for the Toffees.