Apologies often include phrases like: "I know how you feel ...". However, you can't know how others really feel. That only sounds arrogant. First you should ask how they feel.
It's very likely that you didn't want to cause a problem. Others, however, aren't interested in your intentions, but in the consequences of your actions. Omit statements such as: "I didn't want this to happen."
"I would like to apologize." isn't the same as "I am sorry." If you really want to apologize, don't announce your apology. Apologize straight out.
-kk-
Article source ChiefExecutive.net - US website for top managers