What is the properly way to say "I made a mistake due to carelessness", meaning that I did it accidentally and without intent, and I'm very sorry about that?
Something close in meaning to the Russian "Я ошиблась по невнимательности" or "Я совершила ошибку нечайно".
To make the context clearer: at work, I did not fully understand the client's requirements, and did some of the work wrong, and later I may have to discuss this in a meeting with the client.
There are many words that look almost like synonyms for "carelessness" to me: inattention, inadvertence, remissness, thoughtlessly and so on. What are the differences in the use of these words? What can be used in this situation? Which one fits best in my case? Might it be better to rephrase this with more words?