Don't be too hard on yourself. I've never met a bigger obstacle in paramedic practice than my own nerves and internal critical narrative. Also, everyone has those day/weeks and god forbid..months where they couldn't hit the back side of barn with a 22.
A few points that have probably already been mentioned.
Cannulation is seems to directly correlate with my level of confidence. When this happens I find someone to have a laugh with, I sink a few beers, remind myself that s**t happens and start again the next day.
I once came across a senior paramedic that said, any time you miss a line, its is because of a lack of preparation. Mostly, I agree with him. There will always be the 240kg diabetic or the 20yr IVDU who you can't stick. However, I agree that most of the time I've pranged lines, it turned out I wasn't that comfortable with the deal before I pierced the skin. Set yourself up for success. Turn the lights on in the house, open the window, slap them silly, take your time, select a good vein, ANCHOR THE VEIN WELL, have them bring the piano chair in from the other room so u have a better seat (did that the other day), drop the arm bellow the heart, irritate the vein, have them clench their fist... all that usual stuff. Then when you like what you see...have a crack.
Remember despite "ANCHOR THE VEIN" being bolded, simply squeezing or stretching more doesn't necessarily equal more anchorage. Pt appropriate variable combinations of stretch, press and hold may be in order.
For labile or fragile veins, swift and confident is the trick I reckon. The temptation is, the more subtle or fragile the vein, the slower and more careful you are.
The other thing, I think, is once you've got a flash and you drop the angle a bit and want give it that final advance, lift the vein. Move the cannula essentially parallel to, but further from, the skin so that you're launching that final advance into friendly territory and not across the border.