That's not quite the case, I'm afraid - what you "feel" and what you'd experience are two separate things, dependent on your craft's velocity and acceleration at the time. Because your immediate physical reference frame is the ship, you have to take into account what it's doing, and what you're doing.
If your ship was in free-fall (ie not thrusting at all), you'd feel, well, like you were falling, even though you're experiencing gravitational pull. If your ship was thrusting to perfectly counteract that gravitational pull, then you'd feel the gravitational acceleration on your own body as the ship acted against it. (This is the same feeling you experience everywhere on land, and on airplanes that are not ascending or descending. We are constantly resisting one gravity - 1g - acceleration, due to the simple fact that our feet can't pass through the floor.)
And in a combat situation, with widely varying acceleration vectors, your experience would be roughly the same as your ship's, but what you feel would be a different matter. The immediate analogy is, of course, air combat - load up a modern fighter game and watch the G-meter change. 1g is normal - you feel like you would on the ground. 0g is freefall, >1g makes you heavier, <1g tries to smear you on the canopy. Granted, it's all relative to the bottom of your aircraft, since that's the plane in which jet fighters maneuver best - in efficient space combat, the thrust vectors come from every-damn-where. And there's still the gravity well.
A proper artificial gravity would have to: 1. Provide a "down" in a convenient direction, like towards your bum when you're in your chair. 2. Negate acceleration vectors felt by the pilot due to ship motions. What most people take into consideration with inertial dampers. 3. Negate acceleration vectors due to local gravity wells. Acceleration due to gravity is still significant at orbital altitudes (indeed, it's why orbits happen), and for atmospheric flight it might as well be equal to ground level.