You must know that both Docker and Kubernetes are strong tools which are really growing in the market. As I have worked on both in production. Talking about the drawback of both then from my point of view these are as follows:-
Using Database as a container: There is a lot of complexity in using the database as a container. Whether we should go with a container approach for Database or not? If you are using containers for database what is the best way of making data persistent. You need to think of this complex thing.
Networking: By using Kubernetes, there is a lot of development happening in the networking perspective. Like support for flannel, calico, weave etc. But due to the use of NAT its affecting latency of the network. So the question is how we can utilize this tool in business-critical applications? Future development will definitely solve this problem. You can join the Docker and Kubernetes community for more update. If you want to make your career in Docker or Kubernetes then you must take up the following Docker Training Course. For your reference, I am also mentioning a video tutorial on both Docker and Kubernetes which you must watch to clear all your doubts. .