I have an ESC and a brushless DC motor. I am interfacing the ESC to the motor. But I am not getting what I want, so my question is, can I directly connect the motor to the battery without taking the ESC into account?
No, you can't. A brushless DC motor is very similar to a three phase AC induction motor. You need to use a brushless DC motor controller (ESC) designed to generate the rotating field. A DC motor with brushes can indeed be run directly off of a battery (if it has a Permanent magnet field), as the rotating armature has a commutator to keep the armature developing torque against the fixed motor field.
A Brushless DC motor is, as I say, more like a three phase AC induction motor, except that the rotor doesn't turn by developing an induced current and magnetic field, rather the rotor has a permanent magnet which is driven by the rotating field. If you just apply DC to one of the 3 windings, all you would do is (possibly) move the rotor to align up with the magnetic field from that one winding, and then the winding would (most likely) burn up since it would appear as a dead short to the battery.
Also, most brushless DC motor controllers (ESC) are 'choppers' that limit the current sent to the motor, preventing thermal failure. So if you have a '12V' BLDC motor and connect it directly to a 12V battery (no ESC) not only won't it spin (as mentioned above), but I'd expect to permanently damage the windings. Since a stationary DC motor generates no back-EMF, the full battery voltage will be continuously passed over one resistive winding, generating lots of problematic heat.
No you cannot run a brushless DC motor straight off a battery. Brushless DC motors are not really DC motors. The reason they are called DC motors is that their performance characteristics resemble a brushed DC motor (fairly linear speed/torque curve, fairly linear torque/Amp, etc.).
A permanent magnet DC motor can run off DC power because it has a mechanical commutator that physically switches the polarity of the current in the windings so that the magnetic field produced by the windings is always correctly aligned with the magnetic field from the permanent magnet.
A brushless DC motor doesn't have a physical commutator so it needs some method of switching the direction of current in the windings. That is one of the roles of a brushless motor control. (Note, I'm using the term "brushless motor control" as it is a more general term than "ESC," which stands for electronic speed control. ESC is a term that is mostly used in the RC hobby community and generally refers to limited-function controls that provide open loop speed control using zero-crossing, back-emf detection algorithms.)
A brushless motor control switches the current in the windings based on the position of the rotor. There are different ways to determine rotor position (encoder, hall effect sensors, back-emf zero-crossing detection, field oriented control, etc.) but all brushless motor controls require some knowledge of rotor position to function properly.