Whichever pitcher they had used instead of Neris (either in the 8th or the 9th) might not have been available tomorrow either. And if it had been, say, Hutchison, and he gave up two runs, what then? Yeah, Kapler seemingly wanted Neris to get the save, which is traditional, but he also put his closer into the 8th inning of a game in April, which is not.
I guess they really were done with Milner if they couldn't use him, since they already knew he was the one guy who didn't need rest for tomorrow. Or was the roster move already done?