Say that, Russia lost the war in 1877-78 against the Ottomans. How much will it harm Russia ?
IOTL, the victory wasn't overtly celebrated, and in fact granted Russia a lot of disappointment. It didn't worth the lost of many men and material to simply get a largely decreased Bulgaria, which proved later to be troublesome anyway, and a lot of other gains being stripped from them by other powers. The war was generally viewed as a mistake, and later Russian efforts was concentrated to recover from exhaustion and harm caused by the war.
Had the war been lost, means that her prestige will drop low, suffer from immense shock from losing against the "sick man", and face a humiliating indemnity obligation towards the Ottomans. All that will shake domestic politics pretty hard. Expect Alex II to die sooner, and thus earlier ascension of the next Alex. Also, she will perhaps be losing appetite for active involvement in Europe.
How will Russia develop from that point on ? In OTL, Alex III embarked on centralization, Russification and sociopolitical counter-reformation. In a more turbulent political situation, I can see these pursuits will be pushed harder, generating greater backlash. Especially if some subject non-russians will cause trouble, like the Poles. Ditto leftist and anarchist terrorists. Might we see a shorter reign of Alex III ?
Or perhaps, the blow of prestige Russia has suffered and the resultant chaos will convince him to carefully compromise with modernity in part to restore Russia's standing in the world, and in part to appease resentful populace ?
For diplomacy, I still don't see Dreikaiserbund lasting, with neither Frederik III or Wilhelm II was particularly fond of Russia, nor Alex Jr. of Germany. No Balkan issue however, except from Romania and little Serbia which won't be worth warring over. In general, there will be less friction with other powers. Alliance with France will may still happen, but perhaps less motivated, and relations with Germany will be mostly cold shouldering each other, until Willie does something stupid. Austro-Russian relations will be much better with much less clashing interest. Of course, this remains subjected to situational changes both domestically and internationally. But no playground to compete for will influence how the war will be perceived, and perhaps change the alliance make up vis a vis OTL. Eventual Austro-Russian alliance against Germany ?
Another big change I think will be on development of military and physical infrastructures. There'll be more pressing awareness to modernize armaments, tactics, and doctrines. Since there will be less opportunity in Europe (no balkan playground), will Russia move faster towards Pacific and Central Asia ? Might be that Russia be more prepared when they'll have to clash with Japan ? Or more over, will it even affect Russian performance in Boxer Rebellion ?