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."
Why do you assume it is YOUR responsibility to "comfort" this big boy over his "emotional distress" at declining to write the letter for you?
I think it is more like jakebeal said, that his perceived discomfort was at having to refuse the request in person, rather than at not having the time to do it.
In my experience, professors who feel very strongly about a candidate will MAKE time to write a recommendation for them.
In the meantime, you should accept that:
1) This professor, for whatever reason, did not feel strongly enough about you to make the time. He may simply have poor eyesight and couldn't remember who you were, did not successfully connect you in his mind with who you were as a student. When you ran to him after the meeting, he may have been embarrassed about it. Or he may simply have been deep in thought about a particular problem and distressed at having his thoughts interrupted.
2) This professor does not require any comforting from you.
On the positive side, your enthusiasm and confidence should serve you well, so keep your assumptions and move forward. You assume that the professor valued your work but didn't have the time; keep the assumption that your work was highly valuable, whether or not this professor realized it. Keep the assumption that the failure to recognize this is the professor's lack of awareness and is his problem.
While it is wonderful that you want to comfort others, be careful not to overdo this in situations that do not call for it. Make sure you are fully using your attention and energy first to strengthen your own foundation, before giving this kind of energy away to others.