Two issues here:
1) Even if they "learned" something from Koeman sacking, they should have been sounding out replacements since late September. Again, absolutely no foresight whatsoever. Spurs sacked someone and later that day replaced him. Arsenal sacked their manager and had a "caretaker". Watford...well, they are shambolic but at least, again, THEY had foresight.
2) Don't you think that's a bigger issue? If they players are still "playing for him" and we still cannot find a way to win, doesn't that suggest the man setting them up has no idea what he is doing?