The eye test is sufficient.
If you choose to sit deeper as a block, it means that when you win the ball back most of your team, and theirs, are situated in one half of the field. The congestion alone makes playing football on the floor very difficult, especially if the team don't possess excellent ball-carriers. This is why possession proponents, for example, believe in their approach, because if you lose the ball in the opposition half, they're all usually in front of you and passing options are going to be very limited if the opposition tries to play it out under those conditions.
It would be understandable if England were pushed back, but even early on in the first half we shifted back further and further looking for decisive counter attacks. In one half I can't count the amount of times, deep with the ball, we hit Sterling long and high and he sprinted relentless every single time. It's not emotional or ideological to surmise that sprinting from within your own half to the oppositions box is significantly more difficult than say Perisic sprinting off the ball from 10 yards in the England half to the edge of the 18 yard box.
Again, the deeper the team has more pitch in front of them to sprint into. The larger the distance between the defensive block and the forwards, the more isolation there is and more chance that Croatia will sweep up second balls, which is precisely what happened in that game. Sprinting half a field for a long ball, repeatedly is much more likely to result in fatigue than the short distant sprints which Croatia engaged in confined to one half of a field.