Absolutely I did, my melee attack button controlled that sequence. That sequence could have been interrupted at any point by anything. You're classifying that as a QTE? Strange. Playing Dark Souls I use square the vast majority of the time. It takes me through the exact same move set every single time when I'm using the same weapon.
It just honestly sounds like you didn't get the mechanics down very well. How many times you hit the attack button to kill an enemy depends entirely on what weapon you have. Seriously, I picked this up last night without playing since last year and wiped out a group of hunters in the first Pittsburgh area with little to no trouble on hard. The combat is intuitive and smooth, if you know how to use it.
Case in point, you not knowing how or when to use shivs or melee weapons against a Clicker. If you have a shiv that's at full durability you can always defend yourself against one. Or you can choose not to waste one and die. If you decide to engage in a melee fight without one, you're going to die unless you've upgraded the weapon with a spike at then end.