OP, I would ask your DM a very simple question before you bring up any of the FAQs and such. Technically, your DM is quite wrong. But that may not be the point from his perspective. Right or wrong about the RAW, he may not care. Ask this: Do you believe a creature with regeneration cannot be killed by a phantasmal killer spell because you believe phantasmal killer is too powerful or do you believe a creature with regeneration cannot be killed by a phantasmal killer spell because you believe in following the rules and believe that is what the rules say?
If your DM answers the former, then there is no point discussing this with him. I have a feeling it's more of the former and less of the latter though in any case. If your DM answers the latter, then ask him if he is interested in hearing a cogent argument in your favor. He might not be. He is the DM after all and it is his game. But if he isn't, just make him aware of the fact that you expect him to be consistent in his ruling. Also explain to him that you disagree, but will respect his judgment as long as it is his game.
Many DMs have a knee-jerk reaction to save-or-die spells because they already feel spellcasters are unbalancing to the game. If this is the case, just to avoid any future "surprises," it might be a good idea to try to proactively determine how spells will work in interesting cases like this. Chances are that if he doesn't think phantasmal killer can kill a creature with regeneration, he doesn't think finger of death or disintegrate can, or even magic missile for that matter. Feel free to ask him about as many cases as you can think of before choosing a spell simply so that you know what to expect. If he doesn't want to give you an answer (i.e. he is "that" kind of DM), then just accept that you are playing with a DM who has mercurial temperament and a tendency to make arbitrary rulings.
There are a lot of DMs out there who really don't care what the rules say or why because they have a particular point of view on how things "should" be. I encountered such a DM at a convention this past weekend, who, even after being shown in the 4e PH where it quite clearly said a creature without cover or concealment cannot use Stealth to hide, insisted that the rules were poorly worded and that his creature (which did not have cover or concealment) was hidden to my character since my Perception didn't beat the creature's Stealth check. I didn't press the point for long because I realized he simply wasn't going to change his mind because he didn't care about what the rules said so much as what he thought the rules ought to say. And that's fine. My character didn't die and we (the players) won anyway. We still had fun and that is what matters.