It doesn't take long to create that culture though. Real and Barca, and indeed the rags had years of domination under their belts and a big history of success that made players want to join them. The rags managed to win a hell of a lot because of that culture and mentality (unfortunately). It led to players like Wes Brown, John O'Shea and the like being very good when they were at the club but subsequently dross when they put another teams shirt on under a different manager. Liverpool and indeed the rags are evidence as to how quickly that culture can evaporate - Liverpool live off the history of success but in domestic football no one takes them too seriously. In Europe it still plays a huge part. You know when you play Liverpool at Anfield you're in for one hell of a game, and the players step up.
As you say, we don't have that. But under Mancini we were getting there. The Etihad was a place few teams came and won at - similarly to Stamford Bridge under Mourinho (ignoring this season). We "fight til the end" and have won numerous points late on in games. I don't think it will take long at all for Pep to create a strong culture.
What is key about this culture you talk of is strong management though. The club, the fans they are bigger than the player. Pellegrini has allowed players to perform like they're amateurs in a park without fear of losing their place. Pep will haul them off (as Mancini did) and if they don't perform better in the next game they'll be off again. No one will be safe which means when you play you play well for fear of losing your place in the starting lineup.
I don't want to go back into the Mancini managerial issues and I'm not saying he was better than Pellegrini, who has done the job he was brought into do initially (and only to a certain extent). There will be a difference under Pep and it might seem hypocritical to the boards stance with Mancini. If Pep fucks someone off to a golf course in Argentina and doesn't want him back, he won't be back. The board now have their man, the one they've always wanted and we'll see him backed 100%. Whilst he will not work miracles straight away, blues should be very excited to see what the club now do with the manager they will give the world and more to.