First, I want to be clear... player mood only affects contract negotiation. There is no "team chemistry" or "player is upset so he plays worse"... yet :)
Additionally, I am aware of concerns about micromanagement. I don't want it to be essential to micromanage this stuff. If you want to ignore player moods, you probably can get away with it without suffering too much. If your team is successful, players will want to play for you. In a big market? Even better. That gets you most of the way there. It's not like "players who want to play in a big market will only play in a big market" or "players who want to win will only play for an established title contender" - in addition to not being fun, that wouldn't be very realistic either. You can also disable player mood traits in God Mode, if you want.
With that out of the way, take a look at the UI for the new mood system, from your roster page:
There are 3 things you see are their mood score, mood traits, and probability they will be willing to re-s