I used a variation of the same technique you used (PTC: matching specific colors using the LAB color mode) and this was as close as I could get it.
My question is, since this thread is in the "Free Photoshop Requests" (which is not a help forum), do you want this done for you or are you wanting help in doing it for yourself? Please choose one or the other so I will know where to place this thread. Thanks.
The first thing I did was to desaturate the image using IMAGE > ADJUSTMENTS > BLACK & WHITE. I use this so I can achieve the best possible contrast from the image.
Next I added a color fill adjustment layer set to the (Pantone 712C) RGB values of R:252 G:207 B:166
I set this layers blending mode to COLOR.
(note: You could probably get away without using this step, I did it to get the color closer to what I needed it to be)
This was the result...
This color is of course off so I needed to adjust it.
On a new layer, I created a rectangle using the Rectangle Tool set to shape and the color to the same RGB values of the color fill layer, to be R:252 G:207 B:166
I will use this rectangle as a sample.
I then used the Color Sampler Tool to sample the color of the rectangle and the color of the fabric.
This was my reading on the info panel. Point #1=rectangle and Point #2=fabric.
I then added a Curves adjustment layer.
Just like the PTC video, I used the image adjustment tool of the curves panel and sampled from the 2nd point located on the fabric while I held the shift key + Cntrl/Cmd key.
This created point on the RGB channels.
I then went through the red, green, and blue channels and set the output to correspond with the RGB colors of the rectangle (1st point).
I set the red 252
I set the blue to 207
I set the green to 166
I made a few adjustments and this was the final color of the adjusted image.
My contrast was a little light.
So I added another curves adjustment layer and pulled down the darks.
I changed its layer mask to black.
I then used the Brush Tool set to white and a nice soft brush to brush back in some of the darker areas on the second curves adjustment layers layer mask.
Here is the final image with the rectangle for comparison.
Before getting into a discussion of what methods to use to change the colors in an image, unfortunately, nipun, there is a much more fundamental problem you need to think about. This warning applies to any request (including yours) to change an image to a certain Pantone color.
The fundamental problem is that a Pantone color means specific values for hue, for saturation, and for luminosity. If you change every pixel in the image to these numbers, the image becomes nothing but a featureless solid rectangle of color.
To try to help matters out, about the best one can do is to interpret such requests as changing only the hue and saturation values to the Pantone numbers. Unfortunately, this allows one complete freedom to "do whatever they want" with the luminosity. If one would make the luminosity values of the pixels in the result the same as the luminosity values in your original image, the hue & saturation of every pixel would be perfectly correct, but likely, the image will be much too dark for its intended use. So, one has to use some artistic judgement when deciding what to do about the luminosity. The best way to do this is to know how the image is going to be used.
The same sort of judgment call arises with respect to all the small-scale structure in your original image. Some of it may be real, but my guess is that almost all of it is due to noise and artifacts in the camera that took this image. So, does one reduce this "noise" or leave it in. You called it "pixelerated" (sic), and weren't happy with it, and liked Sam's less noisy version.
So, here's another version that took both of the above factors into account:
a) the hue and saturation should be exactly the same as the Pantone color you specified, but the luminosity (and contrast) is nothing more than what I happen to like at the moment (LOL); and,
b) I suppressed the noise even further.
This is certainly very different from both the original and Sam's equally valid version.
Anyway, these are just some things to think about the next time someone asks you to change an image to a specific color.