Is there any way to make crepes without a proper non-stick pan? I unfortunately ended up in situation where I tried to make crepes in a regular pan - needless to say, I was unprepared and it didn't end up well (they would get stuck to the pan and burn)

I tried using both butter and (canola) oil in the pan to avoid sticking, and in varying quantities, cleaning the pan after each failed attempt (so there isn't any burnt stuff from the previous attempt to cause issues), and varying the amount of milk/flour in the batter

Was there something else I should have tried, or was it a hopeless endeavor to being with?
Crepes were made long before teflon was invented.

I use a quality steel pan and non stick spray. I reapply the spray every 3rd or 4th crepe to avoid sticking.

Everything else is temperature control. If your temps are too high then the crepes will toast and burn before they set on top. If the temp is too low then they are more prone to sticking. It takes some trial and error and the first few are usually wrong- I eat those. 

The temperature is always very low though- between low and medium-low on my stove.