After looking at the FFIV screenshots I can see where the red might be just a little too bright, but it's the second darkest red choice that I have in the original game palette. Even changing it to the darkest red only changes it ever so slightly.
It's not just the colour of the center of the carpet that matters, but also the colours of the decorations that are in the border of it. They are currently way too bright and get in the way. Yes the original FF4 is also like that but it's not as bad, because there is only 2 decorations vertically, not on all four sides, and there is definitely no white outline of the carpet like there is in your screenshots.
Also I suspect part of the problem is because you used an emulator that do not reproduce the NES palette well and uses too bright colours for those screenshots. I might be wrong. Remember, the NES palette is somewhat undefined in the RGB colourspace (it is only defined in the YIQ colourspace) and thus, emus could use the value they want. Nestopia has the nicest palette I think.
The mud on the ground in in my opinion too bright. Although it's not as bad as...
Marsh Cave B3
Those yelow sparks on the ground really gets in the way. It really is disturbing. I don't know, change them to green and leave only a couple of pixels to yellow, or change them to teal so at least it feels darker than this aggressive yellow. Just the skull should remain that bright/yellow.
I may be annoying but I'm really trying to help. Feel free to do whatever you want to.
Since you've worked with FF1 NES yourself, you know the color choices are pretty piss poor in some colors,
None of the work I did had anything to do with the graphics. (Also you can change the palette the game uses anytime.)