Antony uses much verbal irony (says one thing but means another as an indirect means of persuasion). His overall goal is to rally the people behind him, his words, and Caesar, but Antony says just the opposite: "Let me not stir you up / To such a sudden flood of mutiny."
There are three types of verbal irony: sarcasm, overstatement, and understatement. See examples below:
Sarcasm: "The noble Brutus."
Sarcasm: "Brutus is an honorable man."
Overstatement: "O, you gods, how dearly Caesar loved him (him)!"
Overstatement: "...put a tongue / In every wound of Caesar that should move / The stones of Rome to rise and mutiny."
Understatement: "You are not wood, you are not stones, but men."
Understatement: "The evil that men do lives after them."
Understatement:"I am no orator..."