You are wrong here generally and especially with your example. Benitez changed at half time from a 4-4-2 system to a 3-4-2-1. That tactical change changed a lot in the game. Obviously you need the mental strength to believe in winning something when you are 3-0 down, but this tactical change was absolutely key to equalizing.
Pep's approach is great at dominating teams and in the league it works great - but he lacks the edge to find solutions, if the other team is ready to stand up to that. A bit of luck is always involved in such games, but then even Leeds can win against City.
And Ole's ability to get United winning should not be overestimated - he has an approach that makes matches quite open, both teams can score and most often United does score more. This is a bit of mentality, but also a lot due to tactics - United could also park the bus, play very cautious and would presumably win as many games as they do, but would not so often have to chase games.
I mean that's fair.
Ultimately though, Pep's inability to change tactics when its needed and change the gameplan to something that is required to win a cup match/final/semi final is something to do with Pep's own mindset isnt it?
His possession football in his formation is a different level of consistency to what most other clubs he plays in a league. Most of the time it feels like Pep's city's, tactics and style of play is too good for other teams and they play at their own will - Peps will.
However what happens when that needs to be changed? Does City's possesion football stop? Do they have someone who can put a performance like Roy Keane vs Juventus 99'? Gerrard vs Milan 2005 final? Could Roy Keane play his Juventus game when playing for a strictly possession based team?
I just feel the players are too busy focusing on their "amazing tactics" that some of the other things that can benefit you in football is forgotten or hidden behind it.
Part of that is the mindset of Pep Guardiola which effects the mindset of the players. Winning through possesion or really not much else.
In the last decade it was obvious that Pep was going to do good in the PL, but when you look at how quick Klopp won the CL - I can say that the Liverpool players have the ability to die for their club and manager whilst what do City players do? Die for their manager or concentrate on playing a better version of Possession based football when its needed?