"Is there a simple way to avoid this, or at least make a "general" improvement?"
Yes, kinda sorta maybe..
Here's the thing. Even if you set you calibration to sRGB, process in sRGB, and post those files tagged with the sRGB color space.. there will still be a significant difference when you view it in your browser.. even on the same machine you processed the image on.
For some, especially those of us who maintain websites and get our prints made at a lab that uses sRGB Fuji Frontier (or like sRGB machines) getting a 100% match has always been sort of the holy grail.
Depending on your monitor, your calibration hardware/software, your skill.. you can get varying degrees of "closeness" and this is what most have lived with.
What happens is some 'stray' amount of color outside the sRGB gamut makes it through no matter how hard we try and this puts a cast over the image. When you get this far, you might see on your browser what you see in your image software.. but on another computer all bets are off.
Recently.. the last few years.. I'm of the opinion manufacturers are doing much better at shipping laptops and PC's with a very close to sRGB profile already active.. keeping in mind that the average laptop LCD probably renders less than 65% of the gamut anyway.. so while the on-line world full of average joes aren't profiled.. they probably have machines which are pretty close..
However.. now we have better tools. We have displays with "sRGB emulation" mode that sort of clamp down on the sRGB gamut not letting those stray colors get by. I find them very accurate.. I can now process, print, and view on the web 100% the same. However, I'm limited to the sRGB gamut. If I want to take advantage of Prophoto (a wider gamut than even Adobe98) then I can switch to that, process, print in house or our of house to someone who uses Prophoto, and then switch back again to sRGB with the click of a mouse.
So.. if you really want this.. I think it will take an investment in a proper/compatible monitor.
Now that I've went this route I've received many kudo's from my website viewers saying the colors look much better to them.. and most of my viewers are basic and don't yet have profiled monitors. My laptops while not spot on.. are extremely close. Clamping down on the gamut seems to translate well to other machines.
So yes.. you can get what you're asking for. But perhaps not with your current equipment.. which you never did say what it was?
