I have historically been a value bettor, but listening to strategy podcasts lately is getting the best of me.
Good value betting is very important to strategy. And I think a lot of players that would otherwise be winners aren't because they don't value bet enough.
But every bet must be backed by a reason to gain something.
On the river it's simply these two reasons and nothing else...
1) Can a lesser hand call? (This is the definition of a "value bet." You stand to gain the value of villain's call.)
2) Can a better hand fold? (This is the definition of a "bluff." You stand to gain a pot that you couldn't win at showdown.)
After you got raised on the river in the pot, the answer to both of these questions was pretty clearly "no."
Now say we were talking about a board with enough higher cards on it where villain could conceivably have a broadway straight, for example. Then that changes the equation on the first question a bit, but you still have to weigh that against the possibility of running into the nuts as well.
Or another example, if there is a double paired board where you have a q hi flush, would it be worth turning your flush into a bluff to make a bigger flush fold for fear of a full house? That might change the equation on the second question.
In either case, use caution and make sure you know your villain. Do not bluff players that call widely, you instead attack them with value bets. You attack the nits with bluffs.
Hopefully that helps.