Considering the strongly connected component is a good start if graph $G$ may have cycles. However, as implied by Pål GD, every vertex is a strongly connected component of a graph without cycles. We need to do more work to find the minimum set of vertices from which all vertices can be reached.
Here is the outline of an algorithm that does the job.
- Find one root $r$ of $G$ by repeatedly going to the ancestor of a node. Mark $r$ as an wanted vertex.
- Remove all vertices reachable from $r$.
- Go to step 1 unless there is no more vertex.
- return all vertices that are marked as wanted.
Exercise. Given a directed graph (that may have cycles), describe an algorithm that finds a minimum set of vertices from which all vertices can be reached. (Hint, strongly connected components are useful now. Try reducing the problem to the current question.)