No, that would be gunpowder that did that. Bodkin (armour piercing) arrows could only penetrate good quality plate armour at extremely close range and if the angle was good....
The Bodkin-tipped arrow was as much to kill the horse as anything. Once the knight is dismounted he’s much less of a threat.
At Agincourt the French Knights evidently resorted to a charge on foot, either because a significant majority of their cavalry mounts were disabled, or because they saw the futility of further mounted charges.
Even before effective firearms there were disciplined bodies of Swiss & German pikeman that were used to deter heavy cavalry charges. Early muskets were only marginally better than a well-handled bow and a lot less reliable when it rained. So while you're right that the firearm ultimately displaced the armored knight from the battlefield, their ranks had been thinning for some time due to a rediscovery of a combined arms tactical system (indirect fire supporting ranks of pike).