We may be going off track a little here to the discussion, but since it's interesting.
Of course not, no armies in history were made up of knights only, it was always knights at the core with support infantry, archers, conscripts, mercenaries etc. Whilst they are not common and only make up a small percentage in an army, maybe a few hundred knights in an army of thousands, they are typically where all the kings and princes are. Normally most of the causalities are from the grunts/fodder troops and very light for knights, but whenever an important noble gets killed in battle, it means knights died, since you'd almost need to kill an entire retinue of knights before you can kill the nobility commanding it. So whilst historic accounts on actual numbers can be vague, but when they record the high commander who's the most important or the 2nd most important noble in the land was killed in battle and almost an entire army was lost, you can safely assume plenty of dead knights happened, and there's a long enough list of important Polish/Russian/Hungarian Grand Dukes and Princes who was killed in battle with Mongols.
Of course, armor were not as heavy at the time of the mongol invasion as it was in later middle ages when things like gothic plates came into being, but nevertheless, the armor the nobles and their knights had at the time would still be miles heavier than the armor and weaponry the Mongols had.