The first thing to keep in mind is that judges don't all see things the same way. An image that is picked apart by one judge can be highly praised by another. Heck, I have even had one image be praised and do really well in a competition, only to be marked down and criticised in another competition by the same judge. Never take what they say to heart, it is all just one persons opinion.
However, if you are getting the same "underexposed" comment regularly, with different judges, then that is how the image is coming across. You may be aiming for dark and moody, but just looking dark and underexposed. I find that where the darkness suits an image and does enhance the mood, it will get positive comments. However, neither of the images above look, to my eye (remember, just one persons opinion) as if making them dark will make them moody as well, just dark and looking underexposed. Unfortunately, in comps, you don't get to explain what you are trying to convey, the image has to stand on it's own. Your car shot just looks underexposed to me, it would look better with a little lightening up on the bodywork, and if it was my shot I would be looking at the colour and the contrast between the rust and the faded paint, trying to emphasise each with the PP.
You can't take just any image and make it moody by going darker, there are a lot of elements to "moody" and the original lighting and composition play a big part. You need to know the end result you want and shoot accordingly, not just make it darker in PP. Also, even dark and moody images often have something a bit brighter that stands out and make it look correctly exposed (even if most of the image has been darkened down). A dark and moody forest scene can have a small area lit by shafts of sunlight breaking through the canopy for example (you can add them in PP if you are good with it). Try looking at the dark and moody images you admire, and ask yourself what makes them so moody apart from being dark, I suspect that is the area you need to work on.
The river shot looks like you have tried to bring out the white branch, but that just looks too bright (again, just my opinion) compared to the rest of the scene and that makes it the main subject as it grabs all the attention. To me, the river should be the subject, not the branch, the branch gets the attention and then, following the leading line that gives you, takes you to a blown out patch of water.
If you are shooting for yourself, the opinion of others means nothing, PP it the way you like it. If shooting for club competitions then you need to consider how judges think, and often how a particular judge thinks (it doesn't hurt to see who is coming in to judge a comp, and google them to see what, and how, they shoot and PP)