That’s about normal Erly.
Depending on if you are using a CRT or LCD display, pictures will always look ‘different’ compared to playing the video on your TV. The TV is the least accurate device in the chain.
Most TV’s when manufactured are setup to a standard test pattern with colour bars and a pattern known as pluge to set the contrast and brightness. The later are effected by the environment you view in. Any changes that you make to the settings on the TV will change from the way it was setup.
Computer CRT displays use a different phosphor coating on the screen, whic responds slightly differently to that of a normal TV and that is also assuming your computer display has been calibrated. The LCD display again displays differently to a CRT and will appear more grainy and often less saturated when viewing video. LCD displays also suffer from smearing caused by the slow response of the pixels changing from light to dark.
The brightness and contrast changes from black to white of the CRT display aren’t linear, it follows an s-shaped curve. This contrasts with the LCD display, which is linear. This will also change what you see on screen. The TV transmission system and ALL cameras are set to work with the CRT display in mind and as such produce an opposite s-shaped curve in contrast and brightness. This cancels out the effect on a normal TV screen. The latest LCD TVs are adjusted to work in a similar way to a CRT TV.
All professional editors use a TV monitor connected to their edit systems that has been accurately calibrated. This is the only sure way to see what your pictures are really like.
As Aanarav says, make sure you have the high quality option set on your Premier monitor window to get the best that can be displayed. You will however need a powerful PC and graphics card to keep the quality at it’s highest while running Premier.