Re-watching the game and, while there is a clear structural issue that is holding us back, the system itself is not lacking terribly.
Our ball circulation may not be so dominant on the central trinity (Messi-Xavi-Iniesta) but if the responsibilities are properly diffused to multiple areas then the system can still work. I am fine with Rakitic moving out wide sometimes because Alves then goes inside and acts as a midfield proxy to combine with Messi/Busquets. I prefer Neymar playing to the interior because he can/does act as an attacking midfielder often to be a part of quick passing sequences (re: Messi's goal for example). Rakitic is always versatile and mobile to help out his teammates (Alves/Messi/etc.) and support whatever moves we are building. Busquets now has a greater responsibility in our passing game than he did back in 2011 as well. All of this shows how we aren't so 'central midfield' heavy in our approach anymore ever since Xavi's decline and Pep's departure. That is the correct evolutionary path to take, we're playing to our strengths (the forwards) rather than trying to cater to the old golden days.
The biggest disruption that we've seen is a disconnect between the left/right sides. This is because both of our midfielders are width-based. Rakitic plays like this by design to turn Alves into a faux-midfielder while Iniesta always naturally gravitates to the left. I hate to say this, but I see Iniesta as a big issue here. Even when Alba is level with the back line, he played very much shunted to the left side. Yesterday, it was almost Roberto-esque how he left voids in our buildup sometimes (unless it was on the flank with Alba). Though his defensive presence is larger this year, he wasn't 'babysitting Alba' the way Rakitic does and was generally not acting as a consistent outlet for the ball to move between both sides.
This is why I think a player like Xavi is the way to go for big games to help us actually 'control' the midfield. With the likes of Neymar, Messi, and even Alves acting as creative attacking midfielders to be direct, our central midfielders need to be the platform/support system to circulate the ball through all zones. Rakitic does this for the right, Busi as the pivot, but Iniesta isn't much of a distribution outlet and that creates a divide in our midfield that leaves us approaching the flanks all the time from either side instead of having a connection in the middle. Xavi on the left, as seen against Granada, will always make himself available and combine with Rakitic in central areas so that we do have better control. 3 foundation/supporting players in Rakitic-Busi-Xavi with 3 attack minded midfielders playing centrally/wide in Neymar/Messi/Alves and the extra men (Alba supporting the left flank, Suarez in the final third). I believe this formula for big games will work much better as a unit than Iniesta-Rakitic which creates a split that weakens our domination.
Defensively, it was all managerial/player errors. This calls for improvement but it's not a 'fundamental' issue (except I would highly advocate for a tactic of playing Mathieu on the left and Pique-Vermaelen/Masch/Bartra in some big games).