Mark Antony is alluding to the fact that evil deeds in history are often more easily remembered than the good ones. A cursory dip into any history book will confirm this. One of the purposes of Mark Antony's speech is to mitigate any evils that Caesar may have committed while highlighting the good that he did.
Mark Antony's immediate audience consists largely of plebs, who, for the most part, loved Caesar. Indeed, it was their love for him which stirred up the ire of Brutus and the other conspirators. They hated Caesar for pandering to the mob, which they saw as an example of his overweening ambition, expressive of an ultimate desire to crown himself a king. As his audience is sympathetic, Mark Antony uses pathos, or an appeal to the emotions, to rekindle that love of the people for their fallen leader, as it may soon fade in the enveloping confusion of a rapidly-changing political situation.
It is often said that history is written by the victors. In the immediate aftermath of Caesar's assassination it is the conspirators who are the victors. And as such they are keen to rewrite the history of Caesar's rule to their advantage. Mark Antony's speech is a subtle attempt to stop them from doing this. Not only is he absolutely determined to ensure that Caesar's good name will live on, he is also going to do whatever he can to make sure that the evil of the conspirators, their bloody act of treachery, will not only be punished, but never forgotten.