The end of the Abbasid caliphate managed to be both somewhat anti-climactic and historically pivotal at the same time. In any practical sense, the caliphs had stopped being politically relevant in 945, when the Iranian Buyids seized Baghdad and put the caliphate under their “protection.” Even this was really the end of a process rather than a sudden change. The Abbasids had been losing control of their empire–to local dynasties, to the rival Fatimid Caliphate (which took North Africa from them in 909 and then Egypt in 969), and even to their own Turkish slave soldiers–for decades before that. The Turkish Seljuks swept in to Baghdad in 1055 and “liberated” the caliphs from Buyid control, but all that really meant was that the caliphs had to report to Seljuk masters instead.
To be fair, successive caliphs were able to exploit the breakup of the Seljuk Empire to assert some direct control over parts of Iraq, starting in the early-middle 12th century. But for the most part they had been reduced to a purely symbolic kind of authority–they had the ability to confer legitimacy, but no real ability to control any territory beyond their literal Iraqi back yard. So the final end of this declining dynasty wasn’t exactly a bolt from the blue.
Still, imagine the psychological shock to Muslims around the world to see Islam’s greatest city and its symbolic leader brought down like this. I don’t think we have any modern reference for it–maybe watching the Nazis march into Paris, though I don’t even think that does it justice. Constantinople’s fall to the Ottomans was probably comparable to some degree, although the Mongols were more sudden and surprising in their conquests than the Ottomans were in theirs.