The knight definitely was the decisive factor in battles during a certain period. When society was almost completely feudal, from the 11th century till the 13th century, knights were the exclusive elite warrior caste. In those times there were no significant cities or trade. The bulk of the people worked on the lands of the nobility. The nobilitys only purpose was warfare, they were trained from childhood to be a knight. The enormous gap in skill and equipment between the knights and the other soldiers, lightly equipped levied peasants, made them the decisive factor in pretty much any battle.
Battles during these times were poorly documented, but also most likely much smaller than the battles between nations and religions later on. Lords pretty much governed their lands independently, wars were quite small. Kings had little power and there was no sense of nationality at all. So its a lot more difficult to find battles like that.
As the feudal system started to crumble, so did the combat prowess of the knight. Cities and trade grew quickly, which tried to free themselves from the restraints of the nobilitys rule. The gap between the peasant and knight, was filled with rich commoners, able to outfit themselves with some armor and pikes and crossbows. Cities had money and mercenary bands started to form, which, like the knight, were experienced in warfare and were much more capable in dealing with a heavy cavalry charge.
Yet, knights were still a force to be reckoned with. Just the fame of those battles you mentioned, shows how much knights were feared and what a exception it was that the infantry army successfully defeated knights, mostly due to poor conditions for cavalry, a good defensive position or extreme fatigue.