I don't think the "would not exist if I hadn't created it" argument really works. If I delegate a project to someone else, and they do the project, does that mean I did it? In my mind, I could comfortably say I managed it, or I designed some parts of it, but I really couldn't take the credit for actually doing it. You wanted it to be done, so you asked someone to do it.
If anything, I would say your conclusion should be flipped: you didn't really do the "making," but you can still be proud of what you _did_ do: provide direction and a vision for a solution to a problem.
What about a director of a movie. They aren't responsible for the creative performances but they are certainly given a heap of credit for having made the movie.
I ask 10 actors for 10 scenes and I combine them into a movie I wanted.
I ask 10 agents for 10 functions and I combine them into a program I wanted.
What's the difference and why is the guy who used agents not credited the same way as a director? Maybe all that's missing is a long list of credits for everyone involved -- so transparency in who did what?
You're honest, but you'd make a terrible CEO in this day and age.