A few quick thoughts from an architectural and technical illustrator and renderer on shadows & shadow colours:
Shadow colour is complex, and is driven by a number of factors: local tone of the object onto which the shadow is being cast, the colours of the various direct light sources in the space, and the incident or bounced light colour contributions from nearby surfaces.
First - the colour and tone of the object onto which the shadow is cast matters most, as does the sub-surface scattering it may have (think of a wax candle for a quick example of sub-surface scattering) - as it does in this case: the marble countertop passes a small amount of light inside itself which re-exits with a tint based on the qualities of the marble. Other local surface considerations are to do with texture - roughness, fuzziness, glossiness, metallic-ness - you get the idea.
Second - the colour or tone of other nearby direct light sources (if there are three main lights in a scene, there are three sets of shadows, and where those intersect you see additive shadow colouring) matters a lot as well, and can profoundly influence your illustration.
Third - the qualities of the light source itself matter - does the light carry a hue, how far away is the light source and thus how hard or soft the shadow (how distinctly visible is the umbra?) and at what relative angle compared to items in the scene? You must carefully match any extant shadows by understanding the primary light and shadow source in detail.
Last - and most crucially to get right when trying for photo-realism (as when compositing, for example) consider colour contributions from incident light - the light being bounced from nearby surfaces which in aggregate we call "global illumination" or "ambient light"... so for example, if a surface is bright red, the nearby surfaces will be tinted red, as will shadows on them, as the surface bounces light to those nearby surfaces.
So all these things being considered, I see:
- The pot's shadow shows far more visible umbra; box shadow umbra doesn't match - clearly a different light source at a different distance.
- The pot has a warm local surface tone, which is affecting local bounced light; the box also has a warm local tone, so we should expect the box shadow to also be warm-shifted - instead it's cool-shifted and thus looks false.
- Our erstwhile compositor hasn't yet learned the ONE quick-n-dirty shadow trick which can help more than ANY other to make colour-matching nearly foolproof: set all shadow layer's transparency blend mode to "Multiply" - this will get you to 80% almost instantly.
If you want more details on umbra and shadow-casting, look at this previous question & answer:
How would I draw a shadow from a spherical object onto a non-flat surface?
After a brief exchange in comments, I thought I should add this:
The use of multiply blend mode can help bring a shadow's hue in line because the black with transparency of the shadow doesn't over-ride the underlying hue of the surface being cast upon - this doesn't at all help with bringing in local surface tone from the object casting the shadow - for that you need to manually add some kind of colour cast yourself - see below.
This was a less than five minute exercise in Affinity Designer in which I have added in total two ellipses and three freeform curves: the sphere ellipse and the elliptical ambient occlusion shadow directly beneath it, the longer cast shadow, the on-sphere shadow and the colour-cast area are all free-form paths. The colour cast path is set to "Hue" and has an elliptical gradient fill taking the two primary tones of the sphere, has a gaussian blur and a transparency fade; the shadows are all straight black, with gaussian blur, transparency fades and are set to multiply.
This is not intended as an exemplar of good rendering - merely to address the specific shadow colour question!
Hope this helps.