@weebopenguin Not really, this will actually be better explained once you delve further into the manga. When a general dies, his men lose their will to fight. That is because of their strong love or respect for their commander, so they get mentally destroyed. No spoilers, but this scenario will continue happening a couple of times in the manga. This is also the case in real life war, whether it be historical or the present.
Also, thinking at it logically, it would make sense for an army to crumble without a general. The general is the one giving orders and looking at the battefield as a whole. When that aspect of an army is lost, it simultaneously loses its ultimate goal and its strategy, thereby all momentum is lost.