A great way to get better greys in to your designs (especially if you design in the browser) is to use Chrome dev tools. In the top right hand corner of the inspector there is a cog icon, this will allow you to choose the colour setting of the inspector. Select HSL (hue, saturation, lightness) the middle percentage is saturation.
Now you can take you primary colour palette de-saturate it (reduce the second value) and boom! You have a awesome grey palette.