Perhaps no defence could deal with Cristiano Ronaldo, but Klopp thought the key lay in stopping the flow of balls to him, so he blocked Alonso.
Too much depended on the Basque midfielder: Real Madrid's transitions were based on his long passes to the surging full-backs or the front four, and the Blitzkrieg-counters were the weapon of choice.
This was pure run-and-gun football.
Jose Mourinho later left the Bernabeu without solving that problem—but also without finding the best role on the pitch for Luka Modric. It became apparent, over the course of the season, that the 4-2-3-1 formation the Portuguese insisted on playing was inherent to the problem.
If he paired Modric with Alonso, that gave the team an additional creative option and rendered it almost impossible for the opponent to block two classy, deep-lying creators.
But the tactic was laden with risk: every time Modric moved forward, he left Alonso very exposed and vulnerable to counter-attacking threats.
If Modric stayed put, the point of playing him in that position was largely lost.
His characteristics weren't utilized in optimal fashion, so the Croatian's attacking game chiefly consisted of keeping the ball and playing short passes. Using him in Mesut Ozil's position also failed to extract his best form.
Carlo Ancelotti graduated from the coaching academy in Coverciano with a thesis on the 4-3-2-1 formation, popularly known as the 'Christmas Tree'. He prefers to achieve domination in the middle of the park and has proven more than willing to sacrifice width for it.
He loves playmakers and has usually had at least two in his starting line-ups.
From the very beginning, the Italian seemed like a perfect coach for Luka Modric. "He's a more dynamic player than [Andrea] Pirlo is," Ancelotti said at his Madrid unveiling, per RealMadrid.com. "They're different. Pirlo has a defined position and Modric plays all over the field."
At first, Ancelotti tried to fit new signings into the old system.
As some Spanish journalists suggested, that may have been partly due to pressure from the club board, who took the decision to sell Mesut Ozil and promote Isco as the true No. 10—the kind of player eternally celebrated by the Bernabeu faithful.
The introduction of Gareth Bale into the starting line-up was simply a matter of time, but considerable playing time also needed to be given to €30 million-signing Asier Illarramendi, who had been brought from Real Sociedad that summer.
Xabi Alonso's injury, which forced the player to miss the first two months of the season, pressed him into early action. Soon after the Spaniard returned to the team, Sami Khedira was sidelined until the summer with an ACL tear.
That was the moment Ancelotti decided to switch to 4-3-3, the formation he had experimented with earlier in the season.
A multifunctional trivote was formed with Alonso operating in front of the back four, aided by Modric and—surprisingly—Angel Di Maria on either side of him.
The Argentinian is an interesting choice: he seemed practically written off following Bale's arrival, but he sometimes plays a similar role for the national team and has been known to operate much deeper as winger than was the case with Cristiano Ronaldo on the other flank.
The switch has proven successful so far and, although Ancelotti still likes to mix it up a bit from match to match, it now appears to be his Plan A.
With this midfield, the team has better balance and a greater fluidity between the lines.
Each of the three players offers good defensive awareness, as well as creativity: Xabi Alonso with his distribution of long passes, Di Maria through vigorous verticality and Modric with his "receive-turn-pass" manoeuvres, keeping himself and the ball in constant movement.
A small digression: when Luka Modric was a kid, a lot of football he played was by himself.
As a six-year-old, he moved with his family to the coastal city of Zadar and lived in a bleak, army-owned hotel. They were refugees, driven out of their home in the nearby village when the war broke out. Sirens, signalling bombing, from the surrounding mountains interfered with every aspect of normal life, and thousands of grenades fell on NK Zadar's training pitch in those years.
We were told about this boy who was kicking the ball around the hotel parking lot all day," the club's chairman Josip Bajlo recalled in an interview for The Guardian.
He was small and malnourished, but had that something special in him. What he used to do was smash the ball into a concrete wall, control the rebound with minimum touch, then quickly turn around and run the other way.
It may be just a theory, but several people in Zadar testify he already had some elements of his trademark playing style when he joined their club's youth ranks, having first developed them on that parking lot.
In later years, he was always the smallest on the pitch, so his primary concern was how to keep the ball and avoid being fouled by larger kids.
You can see those elements in his play now: how he moves towards the ball to receive the pass, how he controls it with a single touch, immediately making a half-turn to create space or evade a challenge.
Although hardly a natural ball-winner, he has made great improvement in his defensive play, with 2.3 successful tackles and two interceptions per game this season, per WhoScored.
Modric is a modern playmaker who belongs deeper in midfield, where he has more space than further up, but mastering that part of the pitch wasn't enough to make him a key player for Real Madrid—he needed to step up and show more initiative.
Now that has started happening on a regular basis.
"His best quality is penetration with the ball," Ancelotti told RealMadrid.com after this season's 2-0 win over Granada. "At the start of the season he showed less character, but now he is showing a lot more."
Modric is no longer inhibited by a reluctance to move forward, because when Madrid are out of possession, there's always Alonso (and usually Di Maria) behind him.
He tries to hold up his opponent and win possession—when he succeeds, he knows exactly how to create space for himself, launch a quick attack and "penetrate" with the ball.
His playmaking style now offers something new in Madrid's transition, changing the spacial configuration of their attacks.
With Modric advancing, Ronaldo and Bale are more prone to cutting inside and playing like the "2" in Ancelotti's favourite Christmas Tree, or moving into the box when he arrives on the edge of the area.
Assists were never a particularly strong element of his game—however, this season the Croatian has already provided six of them in the league, with four of those coming in his last five matches.
With two of the best players in the world as wingers, Real Madrid are, of course, still a predominantly counter-attacking team. But they've upped their average possession to 60 percent, and the run-and-gun football of Mourinho's era is slowly changing into something more subtle and patient.
Luka Modric has been at the heart of that transformation, refuting the Klopp paradigm on "Alonso-dependence" in the process.