How does Brutus justify Caesar's murder when he speaks to the people?

Brutus tells him that Caesar was destroying the republic and had to be removed from power. Antony pretends to be convinced by this and asks the conspirators to, "Let each man render me his bloody hand" (3.1.185). He then shakes hands with each of them, naming them as he faces each man. The last hand he takes is that of Trebonius, who actually did not commit the murder, but distracted Mark Antony so he would not be able to protect Caesar.