You don't need the "But" here in my opinion. Here's the way I would use both words: I know I didn't call you, but I'm sorry. I fell in a well and was only rescued an hour ago.
[Note that you can also use "and" in place of "but."]
Priscilla asked me to call you on July 27 to discuss this matter. I'm sorry that I wasn't able to. [Note that your two original sentences confuse "calling" and "meeting." This version just focuses on calling.]