Extra inning games

Correct me if I'm wrong. But isn't the home team supposed to have the advantage in extra inning games? The Indians just played their third straight extra inning game against a key divisional rival losing two of three. After a while failure to win close games becomes attributable to the decisions made by the manager. I have not reached the point where I would recommend firing the manager (Eric Wedge). However, he must be feeling the heat by now. Something must be done to get the teams attention.