I've experienced a level of "unappreciation" for the design process that I believe stems from a lack of understanding from the client POV. All they see is us giving them something after asking for it, and they don't fully experience the time and effort that goes into it behind the curtain. It's a magic trick for them, and that's a good thing. It means we're doing our job right if they see us giving them something amazing.
One of my favorite blogs for these frustrations is Clients From Hell.It's a collection of shortened client interactions from designers all over the world who experience trouble clients, and more often than not, the difficulty of getting paid for their work. For me, this blog serves as a beacon that I'm not alone in these struggles. It also acts as an outlet for letting off some steam, and enjoying the humor in other people's situations.
The best way to bridge this gap is to have a base of communication centered on trust between you and the client. They hired you to do a job that anyone *could* do, but you're the one who can do it well.
One specific analogy came from a client asking for a logo, and making the comment, "Just open up Photoshop or whatever and whip one out. I'll pay you $25." To which the designer replied, "Ok, do you have Microsoft Word? Write me a novel. I'm willing to pay you $25 for 200 pages, and make it good." It just doesn't work that way.
There are three things clients want when asking for a design. They want it fast, cheap, and good. The trick is, they can only pick two of those things. I actually keep a printed out copy on the wall in my office just in case I need to point and remind a client how it works.