Unable to Play both Fast and Well at the Same Time

Whenever I play daily chess or rapid chess, I am able to get 90%+ accuracy very often (more than half the time). I'm often able to find tactics almost as well as I do in tactics trainer (as I usually have a good idea of what type of positions look tactical and calculate with the time given). However, when I play bullet chess, it isn't uncommon for me to leave pieces (particularly the rooks on a1/h1 or the pawn on g2) en prise, or even move pieces into en prise squares. Never mind blundering forks or skewers or just miscounting the number of attackers and defenders on a pawn. 

How do people here play both fast and well at the same time? It seems like I could do one or the other, but not both. It seems like some people consistently calculate 4-5 move tactics with 1 second per move.

I think its pretty normal to blunder pieces in bullet games. I'm about 2k on lichess bullet and id say I drop a piece every third game. I'm sure people who learned chess at a very early age have an easier time with this issue since its more natural for them to NOT blunder . I mean in the end it all comes down to experience- the more you play, the better you play

I remember one of my lichess bullet games against someone rated 1700s in lichess. It was one of my best bullet games in terms of accuracy, and I think I flagged after we both had a centipawn loss in the teens.