I've long been of the opinion that a manager doesn't have that much to do with the winning of the game once the first pitch is thrown. A pitching change or pinch-hitting for a batter can occasionally determine the course of a game, but over 162 games, on-field tactical decisions aren't likely to influence the final record that much. But I do believe that manager does play a key role in other ways that aren't usually seen by the public.
It's hard to know how well a manager does in getting the most out of his players until you've gathered a lot of anecdotal evidence; for example, if a player who's bounced around quite a bit suddenly blossoms after playing for a particular manager, you could assign the cause of that to the manager just being there at the right time, but when there's a history of many players performing at their best under a manager, then you start to take those anecdotes seriously. The causes could be anything from a good grasp of nuts-and-bolts hitting/pitching mechanics, or it could be the ability to know how to motivate a wide variety of people, whether that variety be cultural or in the realm of personalities. There have been many successful managers or head coaches who aren't noted as tactical geniuses, but who excel in inter-personal relationships. In fact, I think the managers who have success over a long period of time all have to be good in this area. Phil Jackson has had lots of talent over his storied career, but he also had difficult personalities that came with that talent, and if he couldn't manage those egos in the locker room, then it wouldn't matter how much basketball knowledge he brought to the table.
So how does this relate to Manny Acta? I can't definitively say that he lost the clubhouse, because I'm not privy to that information, and the talent (or lack thereof) on the two clubs he's managed muddles the waters somewhat, but I think that in both cases he wasn't fired because he made the wrong pitching change or played the wrong player. Dusty Baker has had his critics over the years over his on-field moves, but generally his teams meet or exceed expectations, so you can live with the tactical quirks. But I don't think you can live with a manager who can't get through to the players in the clubhouse.
This does not excuse the people who provided Acta with the talent he was working with. The Antonetti/Shapiro team had a very poor winter in 2011-2012, and they should bear as much responsibility for what happened after the All-Star Break as Acta.