So basically I compare Nikon d5100 and Canon Powershoot and image contrast is mach lower on second camera. Is it because of compact sensor quality, or it is theoretically impossible to have great contrast and saturation on smaller sensor?
You are confusing saturation and contrast.
Saturation is a result of the interpretation of the data read from the sensor and varies greatly between cameras. On a compact or even point-and-shoot camera, saturation is often fixed at a relatively high level (some brands are bigger offenders than others). By default, DSLRs most often show more realistic images and have lower saturation than small sensor cameras. This is only a default and can be adjusted in 5 to 19 steps depending on the particular model not including the choice of picture style (or equivalent). If you shoot RAW you can make your own interpretation and process images to be a saturated or not as you like.
Contrast has two components.
One is the DR of the sensor which is where small sensors are very disadvantaged. This is why a DSLR will capture scenes of higher contrast.
The second component is an interpretation of the linear data read from the sensor. This is called the tone-curve usually. With a DSLR you can make your own if you shoot RAW. With a point-and-shoot this is usually fixed to a curve which deliberately shows little shadow details to avoid showing high levels of noise, this cause an image to look more dull though.
Finally, there is Micro-Contrast. This is contrast bewteen adjacent pixels. This is feature of the lens and to some extent the anti-alias filter in front of the sensor. In this case, the comparison wont hold between camera sizes alone. Since DSLR lenses have superb micro-contrast and so are some high-end compact camera's lenses. Some DSLR lenses have very poor contrast and so are some lenses of compacts.
From a theoretical point of view there is an advantage when it comes to contrast for DSLRs as the larger sensors permit larger sharper lenses with better contrast, as well as potentially greater dynamic range from capturing more light. DSLR lenses are usually less prone to flaring and easier to clean than compact lenses. It's also possible that other effects such as shallow depth of field lead to images which seem to have more contrast.
It's not the case however, that the small sensor prevents you from producing vibrant contrasty images. Image processing plays a large part, it may be your compact's default settings are more conservative than the d5100. Variations between brands are also not uncommon.
It's also possible to increase both contrast and saturation in post production - it shouldn't be that difficult to match the unprocessed output of your d5100.