If you are using Stack Exchange sites to find information that helps you complete work-related tasks, document the occasions when you solve a problem based on information that you get from an SE site.
For example, if you are responsible for tasks that are tracked with some kind of bug tracking, ticketing, or version control system, and you find yourself cobbling together a solution from a set of Stackoverflow or Superuser posts, record the URLs to those posts in the notes on the ticket. (You should be doing this anyway for completeness in tracking the issue). Then, you should be able to easily report a real number of instances in which SE has directly provided value to you and your company.
If you are building and expanding your own knowledge base, yet still able to apply the knowledge to work-related tasks, use the conversation as an opportunity to talk to your manager about continuing education. Be specific, and request training around topics and technologies that directly apply to your work and your firm. You may find a way to get additional training and have the company pay for it, in which case, your continuing education time would be sanctioned.
If, however, you find yourself researching subjects that simply interest you, or that you wish you were working with but aren't because of, e.g. company culture, you may want to ask yourself if you are growing in the right direction at your current job. In this case, be honest with yourself about how relevant your Stack Exchange research really is, and whether your manager's advisement might be a good reality check.