Tools specifically for training at finding loose pieces? There are of course lots of tactical trainers out there, but I'm wonder if there are any that focus solely on the basic skill of spotting loose or hanging pieces. It is of course a trivial exercise when given enough time: one could just look at each piece in turn and see if it's being attacked/defended. Under time pressure, it's a different story: I often lose under time trouble not even due to a tactic but due to leaving a piece simply hanging.

I'm amazed that when I show a position to an expert, within a fraction of a second they have already spotted all the loose and hanging pieces, whereas I might take at least several seconds to do the same, and sometimes even miss some!

What I'm envisioning is something that shows a position and says "click on all the loose pieces" and the goal is to solve as many of these as possible within a certain amount of time. In other words, something like the Lichess coordinate training tool (https://lichess.org/training/coordinate) but for loose pieces instead of coordinates.
I don't know of any such tool. A paid membership at ChessTempo might allow you to filter problems for the hanging piece motif. Not exactly the type of tool you imagine, but something comparable.

However I would argue against the usefulness of a tool that you describe for the following reason.

If I play chess (and I presume most other players beyond beginner level as well), I do not scan the board after every move for attacked pieces, which is what you are trying to train. 

Instead I ask myself: "What did the last move change with regard to attacked pieces? There are only a few things that change if you move a piece:


the piece will attack new squares from its new position
the piece will stop attacking some squares that it used to attack on its old position
moving the piece can open lines/diagonals for other pieces to attack something
moving the piece can block lines/diagonals for other pieces


Of course, a move can also interrupt you from defending a piece or can create all kinds of multi-move tactics. You don't need to learn a new way of thinking to include these, as you advance in chess: just rephrase/generalize the question to: "What did the last move change with regard to the position?" Anyway, for the time being let's stick with attacked pieces which is what your question is about.

If you look a bit more careful you will soon recognize some features of chess pieces which make answering the question easier. For instance if you move a rook horizontally, it will still attack squares along the line that you moved it, however all the squares that it attacked vertically change. Similarly for the bishop: if you move it along one diagonal, it will essentially only change things along the other (perpendicular) diagonals.

Also, you can take into account the range of pieces to quickly assess whether something is getting attacked. For instance pawns are very short range and it is very easy to see whether they attack anything. Similarly if your opponent does some moving around far away from any action, behind his pawn chain (e.g. castling), chances are that this does not attack anything new.

So my recommendation would be to go with an incremental approach, storing the attacked pieces (later you will add all possible tactics/strategies) in your memory and update your memory after every move.