Don't get defensive. Don't underplay the other person's feelings and try to wiggle out of the conflict. Just because what you said wouldn't hurt you, those memories and emotions are very real and deserve your compassion.
Take ownership of your words: Include in your apology the words, "I am sorry that my (behavior/comment/tone of voice, etc.) hurt you. Period. Do not add the "but" disclaimer as it cancels out the apology. Communicate your understanding of what caused the distress and admit you are remorseful.
Ask for forgiveness: It's hard to ask for forgiveness when you believe you have not done anything wrong, but that approach communicates a lack of respect for your loved one's feelings. It's just not your emotional hot button. Relationships have a way of balancing out when you practice love and compassion over the need to win every battle.
Don't panic: The eruption may need a cooling off period before your relationship gets back to normal. Sometimes you may need to write out what you said so the apology can sink in.