How does Mark Antony feel about Caesar's death?

Mark Antony was devoted to Julius Caesar. He loved him as if he were his own father. He disguises his feelings when he is meeting with the conspirators after the assassination, but when he is alone with Caesar's body he expresses his feelings eloquently. This is the first time the audience realizes that Antony feels so strongly about Caesar, as well as the first time the audience realizes that Antony is capable of such eloquence.

O, pardon me, thou bleeding piece of earth,
That I am meek and gentle with these butchers!
Thou art the ruins of the noblest man
That ever lived in the tide of times.
Woe to the hand that shed this costly blood!
Over thy wounds now do I prophesy
Which like dumb mouths do ope their ruby lips
To beg the voice and utterance of my tongue,
A curse shall light upon the limbs of men;
Domestic fury and fierce civil strife
Shall cumber all the parts of Italy;
Blood and destruction shall be so in use,
And dreadful objects so familiar,
That mothers shall but smile when they behold
Their infants quarter'd with the hands of war;
All pity choked with custom of fell deeds,
And Caesar's spirit ranging for revenge,
With Ate by his side come hot from hell,
Shall in these confines with a monarch's voice
Cry “Havoc!” and let slip the dogs of war,
That this foul deed shall smell above the earth
With carrion men, groaning for burial.    (Act 3, Scene 1)

Shakespeare here is briefly covering the events that actually took place during the long period between the assassination of Julius Caesar and the defeat of Brutus and Cassius at the battle of Philippi. The word "carrion" customarily refers to animals that have died in the open and serve as food for all the wild animals, birds and insects that profit from their deaths. Antony is calling the dead soldiers "carrion men" because they are likely to remain unburied on the battlefield and will be reduced to skeletons by jackals, vultures, crows, maggots, and other creatures that will thrive on this bounty. Antony is a thoroughly experienced warrior and knows what these scenes look like. 

Mark Antony shows his strong feelings about Caesar's death in his funeral oration. It is because of his powerful emotions of grief and outrage that he is able to speak with such compelling fervor. He moves the whole Roman mob to mutiny, even though they all favored the conspirators when Antony began to speak. Then Antony expresses his strong feelings once again when he and Octavius hold a brief parley with Brutus and Cassius while their armies wait to begin the carnage.

Villains! You did not so when your vile daggers
Hack'd one another in the sides of Caesar.
You show'd your teeth like apes, and fawn'd like hounds,
And bow'd like bondmen, kissing Caesar's feet;
Whilst damned Casca, like a cur, behind
Struck Caesar on the neck. O you flatterers!    (Act V, Scene 1)

So Mark Antony continues to feel very bitter about Caesar's death. It is Cassius whose strong motivation drives the first part of Julius Caesar up to the assassination. Then there is a sort of lull until the second half of the play is driven by the strong motivation of Mark Antony. He wants revenge. If Brutus and Cassius thought there was any hope of avoiding a battle by holding a parley, they were mistaken. Antony has already satisfied some of his thirst for revenge by killing all of the men he suspected of favoring Brutus and Cassius in Rome. Now he is ready to finish the job by destroying Brutus and Cassius along with most of their soldiers on the battlefield. Not only is Mark Antony driven by his own desire to avenge the man he revered, but he suggests that Julius Caesar himself has the ability to act through him and inspire him with his own powerful will.

And Caesar's spirit ranging for revenge,
With Ate by his side come hot from hell,
Shall in these confines with a monarch's voice
Cry “Havoc!” and let slip the dogs of war.