There are two types of systems (I'll call them old and new) that I have seen when it comes to pilot lights. In newer systems (sounds like what you have) you must press the valve knob or a separate pilot button to bypass a safety valve and allow enough gas to come out to light the pilot. Once the pilot is lit, the flame heats up a thermocouple that allows the main gas valve to open. Once all that happens, you can turn the valve fully on and light the main burner. The idea is if the flame goes out (thermocouple isn't heated), the gas is completely cut off to avoid leaks.
On older style valves, you just turn the gas all the way on and light the burner. When you are done, you can turn it all the way down to pilot and only the pilot remains lit so you can easily light it next time. If the pilot blows out, you're leaking a small amount of gas (not good).
So, based on those two descriptions, do you still think that something is wrong? Your description doesn't seem to really match either of those exactly, so something could be wrong with your valve. At the very least, the safety valve that cuts off gas flow if the flame blows out could be faulty. Today that's considered a problem, but years ago it was normal - again depends on the valve design. I would have someone look at it just to make sure nothing else is wrong. Gas is pretty deadly.
Try to light it again with the above description in mind, and if it still doesn't seem right, have it looked at.