Calling a function for each updated row in postgresql

I have a sql UPDATE statement in a plpgsql function. I now want to call the pg_notify function for each updated row and am uncertain if my solution is the best possibility.

I am not aware of any position in the UPDATE statement itself where I could apply the function. I don't think it is possible in the SET part and if I would apply the function in the WHERE part, it would be applied to each row as it is checked and not only the updated rows, correct?

I therefore thought I could use the RETURNING part for my purposes and designed the function like this:

CREATE OR REPLACE FUNCTION function_name() RETURNS VOID AS $BODY$
BEGIN
    UPDATE table1
    SET a = TRUE
    FROM table2
    WHERE table1.b = table2.c
    AND <more conditions>
    RETURNING pg_notify('notification_name', table1.pk);
END;
$BODY$ LANGUAGE 'plpgsql' VOLATILE;

Unfortunately this gave me an error saying that I am not using or storing the return value of the query anywhere. I therefore tried putting PERFORM in front of the query but this seemed to be syntactically incorrect.

After trying different combinations with PERFORM my ultimate solution is this:

CREATE OR REPLACE FUNCTION function_name() RETURNS VOID AS $BODY$
DECLARE
    dev_null INTEGER;
BEGIN
    WITH updated AS (
        UPDATE table1
        SET a = TRUE
        FROM table2
        WHERE table1.b = table2.c
        AND <more conditions>
        RETURNING pg_notify('notification_name', table1.pk)
    )
    SELECT 1 INTO dev_null;

END;
$BODY$ LANGUAGE 'plpgsql' VOLATILE;

This works as it is supposed to, but I feel like there should be a better solution which does not temporarily store a useless result and does not use a useless variable.

Thank you for your help.

** EDIT 1 **

As can be seen in @pnorton 's answer, a trigger would do the trick in most cases. For me, however, it is not applicable as the receiver of the notifications also sometimes updates the table and I do not want to generate notifications in such a case