Mbappe jumped into a challenge and stamped on Blanco's leg, leaving the midfielder in visible pain.
And he has offered no excuses for his actions and was reportedly "very upset" with his on-field behaviour.
"It was a strong tackle, I spoke with Kylian, he apologized and there is no problem, these are actions that can happen in football," Blanco told the media.
Mbappe is now expected to serve a three-match suspension, but he remains eligible to play against Barcelona in the Copa del Rey final on April 26.