Here's two things that help me personally:

1) It helps if the exposure is something I actually genuinely WANT to do but would usually avoid. If I feel forced into it it's not on "my terms" and so I don't get a sense of control and the anxiety remains. I grow a lot more when it comes from inside.

2) While doing it, pay attention to your mindset. If the mindset is "ok I just have to get through this and then I can go away and relax" then that will not help as much. The mindset needs to be "I will find a way to become more relaxed right now, WHILE I am doing this." Always turn your attention back to your own needs rather than what is required of you or what other people may be thinking/expecting. If the focus remains on "getting through it" the anxiety will also not subside. You want to get away from the mindset of being relieved that it's over and instead trying to break it down into smaller pieces. Like if you were anxious about public speaking, maybe it feels like "okay I have to do the speech and just get it over with" but maybe you want to shift that to "ok first I have to walk up to the podium--good! I did that, what next? Oh yeah, now I have to bring up my slides. How do I do that? Okay, I brought them up." etc. Then you can learn to get better at each step individually and that makes it easier to raise your confidence level.

Usually the anxiety fails to get better if there is a lack of specific awareness of what is happening. So it's important to notice the steps and the details and ask yourself how you are feeling in each moment. Don't know if that helps but thought I'd chime in!