Hmm thats interesting, where is that from?
FIFA Laws of the game, under the Fouls and Misconduct section. The segment posted is 'careless, reckless, using excessive force'. For the foul Pepe committed, I think the 'Serious Foul play' section is relevant:
A player is guilty of serious foul play if he uses excessive force or brutality against an opponent when challenging for the ball when it is in play.
A tackle that endangers the safety of an opponent must be sanctioned as serious foul play.
Any player who lunges at an opponent in challenging for the ball from the front, from the side or from behind using one or both legs, with excessive force and endangering the safety of an opponent is guilty of serious foul play.
Advantage should not be applied in situations involving serious foul play unless there is a clear subsequent opportunity to score a goal. The referee shall send off the player guilty of serious foul play when the ball is next out of play.
A player who is guilty of serious foul play should be sent off and play is restarted with a direct free kick from the position where the offence occurred (see Law 13 – Position of Free Kick) or a penalty kick (if the offence occurred inside the offender’s penalty area).
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The ref is entitled to send off Pepe if he felt the tackle endangered an opponent (the second sentence), and the way Pepe went in, if Alves had followed through as usual, there would've been serious damage.
As mentioned though, sometimes you can get away with a yellow (although I was never, ever that lucky, not even once), but Alves' histrionics might have played a part.
Anyway, in terms of the rules, the ref was entitled to send him off.