The "killed during daytime" is the easiest explanation.
But also, there's a chance his human minions (Renfield-ish characters) betrayed him.
This would make him rage against humanity even further.
Going back to an earlier recurring point, there is nothing wrong with Belmonts and Dracula being related (the "Sonia" argument). It happens in Lords of Shadow (although in a different way) and no one cares there. But bring up Sonia and all of a sudden 'It's such a stupid idea, it would never happen, the thoughy of it makes me barf' blah blah blah. It's huge hypocrisy.
I say, let it have happened, which makes the Belmonts not-so-pure, which enables Dracula later on to do things like Curse them more easily (already shown with Soleiyu, Simon, Richter), and makes the other bloodlines more important (Lecardes, etc.).
Belmonts are only human... they are not the pure holy warriors people perceive them to be.
In this interview, this question is cool:
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USG: I interviewed her (Ayami Kojima) a couple of years ago and she seemed like she'd be pretty interested in working on another Castlevania-style game.
IGA: Oh, really? Whenever I go drinking with her, she always talks about all the times I screwed up before on the games that we worked together, so it's nice to hear that she's interested in that sort of game, working with me again. [laughs] 'Cause the only image I have is all the times I screwed up.
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I wanna go drinking with these people (although I probably would have to know Japanese to do so).