How should you respond to your teacher who cannot help you with a recommendation?
"Thank you, I understand." ... and then let the subject drop.

Also, consider that the expression you say may not have been sadness that the professor did not have time, but discomfort with having to say no to a request in person.  In addition to possibly being true, "I don't have time" is also often used as a standard face-saving code for "No."