You can just reverse the two phrases:

“I felt X, Y, Z, so I did P, Q, R, but I’m sorry for that because it caused you A, B, C.”

Your usage of “but” still invalidates the preceding phrase on behalf of the latter, which works here because the affirmed phrase is the apology.

I don’t think there’s anything wrong with stating your side — but if you mean it, end on the apology.