They are both correct. If I were you. I would go for the first sentence simply because you sound a little more concerned. In the second sentence: "Non ho notato le email che avevi mandato" you might sound like you don't really care that you didn't see those e-mails, while the first sentence sounds a little more empathetic.

Non mi sono accorto dell'email che mi avevi mandato. With the apostrophe you don't know if is one email or more email Usually we use: Non mi sono accorto della mail che mi avevi mandato (one email) - Non mi sono accorto delle mail che mi avevi mandato (more email) Non ho notato le email che mi avevi mandato. (more email) The Giuliano's answer is ok

They have the same meaning. Apart from the fact that the first refers to just one email, while in the second "le email" is a plural ("dell'email" is singular, it stands for "della email", if you want to use a plural in the first too, you should write: "non mi sono accorto delle email che mi avevi mandato") :-)