What settings are you using with your processing, Binnur?
When resizing, I avoid the auto sharpening features like BiCubic Sharpener. Because it doesn't give any personal control over how much sharpening is applied. So I end up with the same sort of effects which you are experiencing.
So, for me, it goes like this.
Do any noise supression while converting the Raw image, or before any other adjustments if not shooting Raw. Noise reduction can cause softness so I'm always wary of using too much. One alternative which I often use is to apply a little bit of Blur Brush which can be carefully applied as and where needed. But it is somewhat time consuming.
Then do my normal sharpening towards the end of processing. Watch out for increasing any noise problems while sharpening. My typical sharpen would be Unsharp Mask around 80 to 120% at 1 or 2 pixels radius at 1 to 3 threshold. But that is just my average settings and there are always exceptions.
When resizing for internet use; that is exactly what I do, a simple Image Size change, not any of the auto resize for the web etc options.
So for CinC use I would resize to 1,000 pixels on the long edge and 96 ppi. Again, this is slightly variable.
Then I might do an extra sharpen if required. Somewhere around 40 or 50% with 0.5 pixel radius and threshold 1.
Other people may do things slightly differently but the principles should be similar.