The problem is in the image itself: It is a jpeg (RAW would give us better editing options) which is already noisy and not evenly lit (you can see that the brightness differs throughout the image). These problems are likely to become even more obvious when editing.
Here is what I could come up with:
It is far from being perfect, but I think that it looks somewhat better than your edit.
How I did it
I added a
Levels Adjustment Layer. I increased the black points for each color channel, namely 91 for Red, 45 for Green and 92 for Blue. Why these numbers? I sampled the background color using the color sampler tool and then adjusted the blackpoints so that each output value is at about 66. This process is further explained here about throughout half of the post ("Color Balance the image")
I merged everything to a new layer using Ctrl+Alt+Shift+E. I converted this layer to a smart object (optional, but recommended for non-destructive editing) and applied a
Camera Raw Filter. In Detail, I set
Noise Reduction to 37 and
Color Noise Reduction to 24.
Color Range to select the brightest stars (select Highlights in the color range window and adjust the
Fuzziness). Duplicate (Ctrl+J) the smart object with the selection active and set the blending mode of the new layer to Screen
You will notice that some parts of the image still appear very purple/pink. I did another selection with color Range, but used Sampled Colors instead; I selected the purple color. Again, adjust
Fuzziness. Based on this selection, I created another
Levels and adjusted the blackpoints as following: RGB 13, R 51, G 41, B 77. You will have to feather the layer mask as my selection was very harsh.
I created a
Curves Adjustment Layer and modified it to form a slight S-Curve.
On top of everything, I added a
Hue/Saturation Layer and set the Master Saturation to -50.
Note that there is no general process for editing (astro) photos. A good technique is to look at your photo, decide what you don't like or what you would want the photo to look like and then do this. Repeat this until you are satisfied.
I hope this helped you at least a bit in terms of showing you new techniques.