Good point. The problem is that this scenario is a common dilemma for visiting managers in games that run into extra innings. Because the home team will always have a chance to tie or win the game in the bottom of an inning even if the visiting team scores the go-ahead run in the top of the inning, a visiting manager will often save his closer in extra innings just in case the team scores the go-ahead run and needs the closer to get three outs in the bottom of the inning.
Ironically (and this is a scary thought for Yankee fans), the ideal pitcher in a long extra-inning game was sitting right in the Yankee bullpen -- Jeff Weaver. As a regular-season starter who hasn't been used at all, he would have been able to pitch as many as six or seven innings if needed. It would have been amazing for this game to come down to this: an inconsistent, often-inept pitcher like Weaver against a dwindling group of Red Sox pitchers running out of gas.