tl;dr: Don't try to micro-manage colour in webdesign.
Every screen is different, every time you use that screen the lighting is different and even the same screen at the same moment may be seen differently by distinct users. Trying to colour manage in such a way that colours are exactly reproduced every time online is a waste of time and effort.
Yes, you can come pretty close by taking colour profiles into account, and you might even get to an exact reproduction of your Photoshop colour in your browser on your screen. Then, you show your prototype to your client, who will look at it either on a mobile device or a monitor that is, in 99.98% of cases, calibrated differently than your screen—if it is calibrated at all.
Add to that the fact that humans' lens slightly changes colour as they age, making them perceive colours to be more yellow the older they are. Add to that the fact that colour perception is changed depending on the intensity and colour of light that falls on the screen it is viewed with. Add to that the fact some screens may be dimmed or brightened because their user prefers it that way. All these factors thwart your efforts to colour manage.
Don't get me wrong, I'm not saying that you shouldn't colour manage and just choose something that's 'close enough'. Try and reproduce your colours accurately, but keep in mind that the Big Wide World™ will do its utmost to shake things up.
Considering that the deviations you are observing are in the order of magnitude of a single RGB unit on a 0 to 255 scale, they are, for all practical means and purposes, negligible. If colours would stray by 10 units or more, I'd start to be concerned. But, even if they are put up directly next to each other on a screen, the vast majority of viewers will not be able to discern between two colours that differ only one unit.
Save yourself the time and effort and just leave it.