How to bring tactics skills into the actual play? According to few popular sites, my tactics rating is consistently about 400 points above my game rating (say, 2200 vs 1800).

Of course, partially it could be a fault of the process: when a tactics engine gives you a position, you know that there is some tactics. On the other hand, I almost always find combinations while observing other people play, in real time - and miss quite many while playing myself. It seems that I become too preoccupied with the plan, or something like that.

Any ideas how it can be healed?
As you have noted yourself, an important difference between solving tactics and finding tactics during a game is that you know that there is something interesting when solving tactics. There are a couple other important differences.
In a game, it comes down to your ability to discern a critical position from an ordinary one that only requires positional consideration. In long time controls, it is advisable that you treat every position as a tactical puzzle, at least for some amount of time. Of course some positions you know are not critical, but spending a little bit of time checking every move will help you be more tactically aware. And of course, you got to watch out for your opponent's tricks too.
I will ignore the question relating to having a 2200 tactics compared to 1800 elo because the scale may be different between the two and an 1800 rated player could have a range of tactical ability anyways.