How should you respond to your teacher who cannot help you with a recommendation? I had a meeting with my former teacher in my former school.
While we were enjoying our tea and pan cake, I saw Prof. Nickname, and we invited him to join us. An hour later, after the tea, Prof. Nickname left first and was walking back to his office. I ran after him and asked if he had time to write a recommendation letter for me, and he told me that he was busy with his teaching and could not write the letter for me. I could see on his face that he felt so sorry about it, and I wanted to comfort him but I did not know what I should say. Given that situation, how would you comfort your teacher who could not 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."