Umbilicoplasty Revision for Slim Patient?

The depth of your belly button depends on a couple of factors:

How short your umbilical stalk was in the first place, and if it was shortened intra-operatively.
How thick your abdominal flap was at the time the belly button was inset into it.

You describe yourself as thin, and certainly if you had a full tummy tuck, your abdominal tissues are stretched even thinner. If your belly button was not shortened intra-op (it probably was not, since you are not obese), then my advice would be to wait until your abdominal tissues relax a bit. Some tissue laxity around the belly button might improve its shape and depth.
I'm sure some of the more experienced surgeons on this forum have some tricks for this problem, so stay tuned for their answers.

Without seeing photos of your before and after, it is difficult to tell you if it would be worthwhile for you to under go an umbilicoplasty revision. There are several things that can create a not-so-perfect belly button after abdominoplasty, and some can easily be corrected, and some are more difficult. If you have lost confidence in your surgeon, I would recommend getting a second and possibly even third opinion. You may end up having more confidence in your original surgeon if you hear the same thing from others, ore you may find someone who can give you the results you want to achieve. But I would advise you to discuss this with your original surgeon so that he/she has the opportunity to go over it again with you. Good luck!

I have observed this in extremely thin patients. It is difficult to create a hooded or deep umbilicus there is no thickness to the walls of the umbilicus.

Your surgeon is right that making a nice belly button on a slim patient is very difficult, because there is no way to create the natural depth. The best thing in my experience is to try to create more of a hood across the top, which can be done under local anesthesia. it's worth giving it a shot because a nice umbiilicoplasty is one of the hallmarks of a good abdominoplasty and I am sure your plastic surgeon want to make it better.

The umbilical appearance is somewhat crucial after abdominoplasty as it is harder to hide than the lower transverse scar with usual summer clothing/bathing suits. The hardest thing to fix afterwards would be an umbilicus that is not on the midline. In fact that may not be completely fixable.
What makes the belly button look natural after surgery is as you stated depth and upper hooding when standing upright but also a more or less vertical ellipse outline with a scar that lies in the depths of the belly button (over the rim). You cannot get that if the surgeon brings the belly button out through a round incision with a scar that runs from the 11 to 1 o'clock positions along the rim. Also if the opening is made to large it can stretch out and flatten the belly button.
If you had posted a picture this reply could have been more detailed/specific.