It's better to say: I FELT regret about something. the rule is, when two verbs come together in a sentence, the second verb is in the infinitive - meaning, uninflected. therefore, the first verb can change its form to either past, present or future form. However, in this case, the word "regret" stands as a NOUN. therefore: 'I felt regret about...' 'I feel regret about...' 'I will feel regret about...' :)

haha No need to feel regret about my absence. Dark Panther is like the force. He will always be with you. :P

No, you can say you feel regret about something, also: I feel regret that no one answers your question. I feel regret at D.P's absence.