Real got Mbappe as a free agent so they couldn't refuse such a player. As for his game, maybe he is not at the peak of his form now, and this penalty could have affected the game, but failures also happen, Salah also couldn't score. Well, Liverpool is in better form now, it was evident from the game, maybe if Vinicius could play, then Real could achieve more in attack, but their defense was also weakened.
Mbappe is a super star player and he is healthy now, at least it is luckiness for Real Madrid that they did not hire a player who is sensitive with injuries like Woodgate or Owen. Mbappe has a lot of time to adapt to his new club, new teammates, new coach and the coach can change tactic, position to use Mbappe better too.
He is under big pressure now because of his ambition and expectation of the club and fans as well, but bringing more critics and more pressure on him, won't help to improve his performances for Real Madrid. If anyone loves Mbappe's football, let's give him freedom and time for improvements.
Real Madrid is not at fault for hiring Mbappe, nor would it be right to blame them. Because, before coming to Real Madrid, Kylian Mbappe's performance was extraordinary. He was a source of hope for the national team and his former French club PSG. But if he cannot perform well after joining Real Madrid, then it is no fault of the Real Madrid authorities.
Perhaps they made big fault by hiring Mbappe even as a free agent, because they have to pay him money for other things. High salary, and other costs for this player too, but they ignored many warnings before the transfer that it's risky to attach Mbappe to their squad. It can potentially create conflicts among star players and on field, it's hard to combine their players with Mbappe. So far these concerns are proven as accurate, and Ancelotti is struggling to use Mbappe effectively while don't affect performances of Vinicius, Jude and Rodrgyo.