What to do if drywall anchor isn't flush with the wall
When ever you are doing Window Treatments such as Curtain rods - the first thing to do is use a SMALL diameter 1/8 inch drill bit and drill a pilot hole for your mounting holes - this way you can know if you hit a stud or only have empty space - typically you can hit a stud because the window framing. 


You will note the pine wood on the drill bit also the force required to drill will tell you if you have only dry wall or a stud.


If you hit a stud SKIP the Anchors the wood stud will secure the screws just fine.

If you do not hit a stud - use a slightly larger bit to see if you are close to a stud - ie catch the edge of it (your anchor might be too wide and you will need to re-position your hole).

Now onto the fact that your screws are short - a hardware store has longer screws , splurge the 50 cents for a pack of longer screws. 

Dry wall patch is sold in stores but for this you can easily get away with pushing in some joint compound (comes in a quick tube as well) - letting it set and then drilling your hole into the stud - use a longer screw 1-1/2 inches should be fine.