One thing the instructors don't want you to do is to "push" the bag. That means you need to "snap" your punch. The same with the backfist when you learn it, don't push, snap it. Speed is the key. Try to remember to hit with only your first two top knuckles (try to make sure that your thumb is under the middle knuckles - look at an ATA patch to see the placement). If you see that all of your knuckles are red, you are punching wrong.
Practice snapping a punch/correct punching - bring punching fist to bottom of your ribs at your side. Your hand is clenched into a fist but palm is facing up. Move fist forward, sliding arm along the ribs. As soon as your elbow is at your side, turn your fist over with the palm down and snap that punch - BAM! If you have a heavy dobok (most of us beginners do not), you will hear your dobok top "pop" when you punch hard and correctly.
I realize when you are doing punching drills, you're probably in a fighting stance but the snapping is what you're looking for. Your strength will build.