Saddle should be level or very close to it. If it slopes down you have to push back.
Make sure your saddle is back far enough. If it is not, then you have more weight on your hands. Yes, it is counter-intuitive, but you are basically balanced on your feet, hands and butt. If your butt is moved forwards, there's less weight to balance your upper body.
Last, the problem with flat bar bikes is that you only have one hand position. With a drop bar you can move to at least three different positions and some variations. That gives your hands and wrists a break since you use different muscles in each position. It really makes a difference on a longer ride.
You can get an additional position by adding bar ends to your flat bar.