What thrilled Capello most was that this outstanding result was based upon the principles of organisation, discipline and courage, which he's championed all his career.
"We now have to play every game like this one - strong, compact, with confidence. Like a team," he said. "This evening I saw one team, a team with spirit."
All true. Some of the ball retention and passing movement, like the intricate four-man interplay which resulted in the decisive second of Walcott's trio just before the hour, could have been made in Buenos Aires.
But it was the individual gift of the boy who didn't even make the starting line-up in Arsenal's last game which did most to forge this new Team England.
A win that came completely out of left field? In truth, it came out of right field.
Every time Walcott got the ball on that flank, Croatia's composure in the stadium where they'd never lost a competitive game in 35 matches over 15 years, cracked.
Walcott also epitomised Capello's brave new world by being utterly selfless, sometimes haring back 40 or 50 yards just to retrieve the ball.
Fortunately, not overly selfless, though. After trying unsuccessfully to cross when he should have shot in the opening minutes, he then remembered David Beckham's advice.
"He'd told me, 'Be a bit more greedy in the box and you'll get goals'. In the end he said I was a bit too greedy!" laughed Walcott, who's only scored four Premier League goals in 44 games for Arsenal.
So hail another invaluable service from Beckham. Dropped and seemingly condemned to watching a quicksilver successor consign him to history, he could have sulked. Instead, he played the father figure.
"It was great to see," said captain John Terry. "He didn't let his head go down but put his arm around Theo, giving him advice."
Yet when Becks replaced him on 85 minutes, it screamed of a changing of the guard. This is Theo time as Arsene Wenger has long predicted.
The Arsenal boss always said those who dismissed England's youngest international as too fragile would end up being silenced.
Of course, the tribulations of another one-time teenage tyro, Wayne Rooney, inform us that his ascent won't be plain sailing so there was a lovely irony in how Walcott's coming of age should have also helped fire Rooney's rejuvenation as he broke his 11-month international goalscoring drought to put England three up.
Five minutes after Croatian substitute Mario Mandzukic had reduced the deficit through England's one moment of absent-mindedness all night, the pair combined to seal the rout in the 82nd minute, Walcott finishing the job with his left foot because his right boot was falling apart and had a stud missing.
It was the first England hat-trick in a competitive fixture since the fabled feat of Michael Owen - remember him? - in Munich.
Recalling how he'd been part of that false dawn under Sven, no wonder Rio Ferdinand pleaded to reporters: "Just don't go overboard with all this, please."
Fair enough, then. We'll note that it could have been different had Robert Kovac not been sent off in the 53rd minute for the careless elbow which forced Joe Cole's substitution and left him with 10 stitches.
We will also dutifully report that Capello dismissed it as "a good performance - but it's nothing".
Yet, sorry Rio, you have to allow us to get intoxicated by the whiff that Fabio might just get it right at last. And anyway, nights like Munich 2001 and Zagreb 2008 are so rare they have to be cherished for their own sake.
Just ask the boy wonder. "Yeah, I remember watching that game," recalled Walcott.
"Funny, here I am now involved in something like it. Munich was brilliant - but this is definitely right up there with it."
