Water pooling between flower bed and clay lawn

Hello

I’ve recently created a flower bed on a slope down to my clay lawn. We mixed in manure to the beds and dressed with bark.

After the irrigation system has run, the bed is nicely moist, but the lower part (next to the lawn) has pooled water and I fear will cause the plants to rot.

Does anyone have any experience creating drainage away from the beds such as these? What is your advice?

Many thanks
H