The murder of Archduke Franz Ferdinand was not "an excuse" to start a war. Serbia in 1914 was a rogue state, the murder of the heir of the Austro-Hungarian Empire and his wife was the result of a conspiracy in which senior officers in the Serbian army were involved. One of them was "Apis", the head of their Intelligence service. Austria had a very strong case to occupy Serbia and put some order in her backyard.
Russia simply had no business there. Douglas Smith in his book Rasputin writes how Rasputin opposed the war until it was declared.
"He [Rasputin] told the Petersburger Newspaper on 13 October 1912:
"What have our "little brothers" about whom our writers screamed, whom they defended, shown us? [...] We have seen the deeds of our little brothers and now we understand [...] Everything [...] Yes [...] As concerns all those various alliances there, well, alliances are good, as long as there's no war, but once war heats up, where are all those allies? They're invisible.
So, fine, dear man, you, by way of example, but look! There's war in the Balkans. And so writers begin to shout in all those newspapers: Let us have war, let us have war! So we, naturally, must fight [...] And they have been calling everyone to war and stoking the fire [...] So I then would ask them [...] I'd ask those writers: "Gentlemen! Why are you doing this? Do you think this is right? One must try to dampen passions if there are tensions, or it'll lead to a big war, and not enflame people's anger and hatred."
And after the murder of Franz Ferdinand in Sarajevo, with Rasputin recovering of an assasination attempt (he had been stabbed in his village of Pokrovskoe by a follower of one of his enemies, the monk Iliodor), he kept sending telegrams to the tsar trying to prevent the war.
"On 12 July [Old Style, 25 July 1914 NS] Rasputin wired Vyrubova: "A serious moment, there's a threat of war." The next day he cabled again, urging her to tell the tsar to avoid war at any cost. On the following day, 14 July, he received an unsigned telegram from Peterhof, most likely from Vyrubova, asking him to change his mind and support the calls for war: "You are aware that our mortal enemy Austria is preparing to attack little Serbia. That country is almost entirely made up of peasants, utterly devoted to Russia. We shall be covered in infamy should we permit this shameless reprisal. If the occasion arises, use your influence to support this just cause. Get well soon."
Rasputin, a Russian peasant, didn't buy the official version of "brave, little Serbia", peopled by "good Orthodox peasants".