He may have a strong sense of responsibility, but to me he seemed a little rude and selfish.
責任 is responsibility. If you add 感 you get a "feeling of responsibility." That's not really a thing people say. What people do say, however, is sense of responsibility. Do you have one?
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.