In the matches lost to Barcelona (first leg of Copa del Rey) and Bayern Munich (first leg of Champions League), Madrid were undone by sucker-punch goals that came when Madrid were in a good position of control. That isn't to say that they weren't deservedly conceded to the opposing team, but it's to say that they were preventable; better personnel can ensure that the mistakes aren't repeated next season. At present, I cannot think of a good secondary formation to recommend for Madrid toutilize, because the 4-2-3-1 is truly the best fit. The latest in the sports world, emailed daily. The idea is that once the defense is able to dispossess the opposing team, the holding midfielder (usually Xabi Alonso) is able to get the ball up quickly to the team's attackers, who then link up quickly with each other to catch the other team's defense unprepared. 
If Madrid intend on making any transfers this season, they should all be defensive.
The team toppled Barcelona, regarded by many as the best team in history going into this season, and broke numerous records on the way. Generally, the idea behind the formation was to be extra-defensive and completely stifle the flow of football in the midfield, hitting the opposition on the counterattack using the skills of Cristiano Ronaldo and two of Karim Benzema, Gonzalo Higuain and Mesut Ozil. However, I would urge Mourinho to put Xabi Alonso alongside Nuri Sahin a try for just a match, to see if they can compliment each other. In 36 out of 38 La Liga games, all 12 Champions League games, four out of six Copa del Rey games and both Supercopa matches, Real Madrid utilized a 4-2-3-1. The Argentinian winger was great at the start of the season but slumped badly after returning from injury. Without covering defensive or holding midfielders, Madrid's defense would likely find itself very vulnerable to counterattacks, especially by teams set up to exclusively counterattack for goals. Even at defensive midfielder, acquisition of a no-nonsense defensive midfielder like Nigel De Jong, Daniele De Rossi, Yaya Toure, etc. Los Blancos also set records with 32 total wins and 16 away wins this season.
On the defensive end, however, Real Madrid's tally of 32 goals allowed is not that impressive and surely can be improved on. Luckily, Sami Khedira and Xabi Alonso have done a good job this season covering the defense, ensuring that Real Madrid's defense was fairly solid over the course of the season. First and foremost, it is arguably the ideal counter-attacking formation. 
When your offense scores 121 goals in a season, there's clearly not much room for improvement. Records are nice, but memorable seasons are defined by silverware in football, not records. In reality, though, the combination of Xabi Alonso, Lassana Diarra/Pepe and Sami Khedira wasn't enough to do much of anything. When Gonzalo Higuain plays alongside Benzema and Ronaldo, the players are even less locked into their positions. Marcelo and Sergio Ramos are renowned for being attacking full-backs, and even Pepe enjoys venturing forward at times. Villarreal benefited from Real's inability to create scoring opportunities with just three genuinely attacking players, while Malaga were disheartened once Real scored the goal they needed to assure progression to the next round of the Copa del Rey. Finally, the formation provides a decent amount of cover for Real Madrid's offensive defenders. Two of the best examples can be seen here and here(Real Madrid's second goal here). Secondly, the 4-2-3-1 gives the team's four attackers a great deal of freedom, which works well for Real Madrid, since Cristiano Ronaldo rarely stays out wide, and Karim Benzema and Mesut Ozil often drift out wide.. With that in mind, we begin our evaluation of Jose Mourinho and Real Madrid's tactics this season. In the four games this season that Mourinho chose not to utilize a 4-2-3-1, he used a 4-3-3. What led to his failures in the Copa del Rey and Champions League? This has worked to perfection on numerous occasions this season.
They recorded 100 league points in a single season, scoring 121 goals and recording a plus-89 goal differential along the way. How can Madrid improve next season? Four games is a small sample size by which to evaluate the success of a formation, but I'd make the argument that this is not a formation Mourinho ought to adopt again next season. Even though I did say that little should be tinkered with on offense, Mourinho will have to figure out what to do with Angel di Maria. That's simply not acceptable, and Mourinho may want to try experimenting with Benzema at right wing again if Di Maria is unable to produce. But for the most part, Mourinho chose to keep things unchanged formation-wise for much of the season. Of course, though, the more ambitious Real Madrid fan will wonder how great this season could've been had Madrid managed to overcome Barcelona in the Copa del Rey or won the Champions League. How did Mourinho consistently win in La Liga? He was a non-factor in every Barcelona match he played in, and did nothing versus Bayern Munich over two legs either. Despite failing to win the Champions League, Real Madrid's players and supporters will likely still regard the 2011-12 season as a success. Sami Khedira has shown massive improvement, but he's still not the intimidating dominator in midfield than Madrid wish he could be. The 4-2-3-1 is the perfect Mourinho formation for a number of reasons. I could write an entire article on the players that need to be sold and acquired by Madrid this summer, but suffice it to say that much work needs to be done with every defensive position. This formation wasn't a huge success: Madrid lost to Barcelona in the Copa del Rey, drew with 17th place Villarreal and could only managed tight 3-2 and 1-0 wins over Valencia and Malaga, respectively. would do Madrid a world of good. Mourinho has earned a reputation for being a tactical genius, and indeed, he's shown himself to be just that on numerous occasions this season and in the past. Barcelona dominated the trio, and Valencia still managed to score two goals past Real Madrid's defensive setup.