No, it's the right link. "Express my sorrow at having caused pain" is a more formal way of saying "I am sorry I have caused pain". You are free to claim there

No, it's the right link. "Express my sorrow at having caused pain" is a more formal way of saying "I am sorry I have caused pain". You are free to claim there are some subtle differences (pro tip: there are not), but further nitpicking will make you look a bit foolish, in my opinion. Your choice.