Have you tried dry firing*? I think this is an excellent way to gain familiarity, without the pressure of a shot (eg will it go where I want). Most top shooters trigger quite assertively in prone; they do so consciously when they see the correct sight picture. It's a quick and practised movement, not a jerk.
I think that your nerves are coming out too. Practise will help, as once you realise you can fire more good shoots, you can just get on with the job. I think it's vital not to count your score as you shoot; this doesn't help, and just piles on the pressure. When you 'scope a shot look at whether the location matches your call, and other shots (remember your group can shift, even if your zero was perfect on the sighter). Ignore the scoring rings, except as a quick guide for sight adjustment. If you aren't calling shots, then why? You need to be thinking about this; start by asking yourself "Was the foresight steady, and was the target central". Then think about the recoil, both the direction and the distance. If the muzzle flips in a different direction to normal, the shot may go that way. More muzzle movement often means the shot fell further out.
Also, how is your trigger set up, single stage, or two stage? If it's a two-stage, how long is the first stage, and is there any creep in the second? The first shouldn't be so short you can't feel it, but not long that you can't take it up before you exhale and the sights are on the target. The second stage should not move back as breaks, movement is creep, and unwanted. There is only pressure then the bang; a single stage trigger is exactly the same, although usually heavier for safety. Anschutz triggers are adjustable, so if it doesn't break properly for you, then make it. Get help if you haven't adjusted one before, although pre-1977 triggers are quite simple with only travel distance and sear (creep) adjustment.
Finally is the blade the right distance from your finger? Too long or too short a reach makes it harder to press with the pad at the tip everyone, and to press with consistent pressure, and to press without tensing your arm and shoulder.
*with an empty case or plug in the chamber to cushion the firing pin.