I would recommend exactly the opposite. APIs should be designed to accept parallel/concurrent calls. This makes the API a little more difficult to design since you have to consider detecting overlapping writes but HTTP provides a nice mechanism for Optimistic Concurrency Control for this purpose. When you are designing an API, take the time to think about each operation and how you can control & detect mis-ordered operations.

Well written APIs make this relatively seamless by explicitly stating the concurrency expectations of an operation as well as what the response looks like when two conflicting operations are applied.