There's a difference between explaining your error and giving an excuse. Explaining means taking responsibility for it. Others will respect you and you can carry on with confidence. An excuse, by contrast, prolongs your pain. Listeners will analyze it and probably judge you more harshly.
Say you forget to bring an important document to a meeting. Rather than give an excuse ("Sorry about that. I was shoveling snow at home this morning and I've been running late all day as a result, forgetting things."), explain the situation ("I apologize for my forgetfulness. I treat these meetings seriously, and I will come prepared from now on.").