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.