Piqué has long legs and I'm 100% sure if he marked Luiz instead of Mascherano there, the ball wouldn't go in, I can think of countless situations exactly like this one where Piqué managed to put the ball away. For their third goal, he was not in the right position to stop the cross, which is usual for him as he is positionally awful for a CB (no surprise for someone who became a CB at 26). And in more than one situation he was harassed by Pastore or whoever else. If that's a good game then our standards are pretty low.
The failure in the play was more in positioning by the entire team, than on Mascherano alone, just like it was for the second goal. Not so sure Pique would have done any different than Mascherano did.
For instance, Alves was the one covering the cross trying to deflect it. He jumped but the ball sailed over him. That's a failure there. Alves is too short to be the one trying to head the ball away. Rakitic or Busquets should have been there on the right side, but instead they were BOTH on the left side. Poor awareness and discipline by the team there.
Second goal was much the same. You had zonal markers in Rakitic and Mathieu because of size, but 3 players failed to stick to their marks, chiefly Alba and Iniesta, as a result the far post was wide open for a clean header.
Defending set pieces is as much discipline and tactics as it is size, perhaps even more than size. Barca had poor discipline and tactics in both cases and they got burnt.