This largely has to do with self-identity, and a bit to do with the perception of those aboard and around the Enterprise's computer.
In the episode Q-Who, Ensign Sonya Gomez is perhaps the first and only acting crewmember to treat the ship's computer with politeness, even telling Chief Engineer Geordi Laforge so herself.
"Well, why not? (Say 'please') It is classified as intelligent software." - Sonya Gomez
The rest of the crew doesn't share her viewpoint though - and usually the Enterprise is treated very much like a non-entity, even going so far as to be used as a counterpoint against Commander Data's right to choose in "Measure of a Man". (No direct quote available, but the idea brought up is the Enterprise refusing to be brought in for a refit).
This episode perhaps gives us the best measure of why it is not, generally, considered a "sentient" being. In Data's own defense of his individuality, "self-awareness" is brought up as one of the most important aspects of sentience. In no episode is the Enterprise ever shown such a capacity - despite the probability that it could have the computational ability to become self-aware, and has before very nearly taken on a sort of self-awareness when posessed by some alien force to give 'birth' in Emergence.
Though we should remember that the Computer showed some very infamous sass towards Commander Data in Conspiracy, when he proved to be a very frustrating user to interface with, so it IS possible that Starship computers are more self-aware than given credit.
But, if they are, they do not ever seem to show it, or show any desire to be recognized as individual entities at all. Whereas Moriarty profusely expressed a desire to live and explore outside of his confines, and thus was recognized as "sentient".
Ultimately, then, if the computer IS sentient, then the only reason it hasn't been recognized as such yet is because it has never asked for such recognition. But it is, definitely, capable of being sentient, and classified as intelligent.
And since we are examining whether or not the computer is sentient based upon its creation of a sentient being, let's go over that a bit as well.
Holographic entities are completely separate beings from the starship on which they are created. They are formed by the computer using pre-generated algorithms, and in the case of the Enterprise's computer can result in very complex holographic programs indeed, but they are not connected to the ship's computer once created, except in the Computer's ability to remove them, store them, or add new programming to them. They are essentially independent programs.
If you want some evidence to this, we need look no further than the entire other side of the galaxy, to everyone's favorite independently thinking hologram - The Doctor.
The Doctor is a holographic entity pre-programmed onto the ship, but serves as a good basis for comparing the ship to other holographic programs it creates. The ship is not The Doctor, and The Doctor never identifies himself as part of the ship. In fact, he goes to great lengths to identify himself as a separate entity entirely (a key aspect of "sentience").
We can assume, except for in cases of extreme circumstance (see "Emergence" above), that this is true of all holographic programs. Moriarty's sentience is separate from the Computer's own capabilities. And given the range of things the computer CAN produce on the holodeck - real illusions of distance, physical beings to interact with, flowing water, bustling cities, characters real enough to interact with, and yet it is none of those things. So why then would we say it could not create a sentient being?
Note that I am not saying the computer is NOT sentient - there's some evidence to suggest it might be. But the ability to create a sentient holographic being does not itself prove that the Enterprise computer is sentient. Highly intelligent yes, and capable of an enormous level of extrapolation - but not sentient.