As the two teams emerged for this game, Pep Guardiola could be seen on the touchline, staring out over the turf, eyes glazed, a man seemingly seized by a deafening clarity. On all four sides of the stadium around him blue and white flags fluttered like a magnificent robe, lending the place acertain tranquillity, even on an occasion this febrile, this flammable. Zero hour at the Etihad Stadium, and all was calm.

As the full-time whistle blew, all was calm again. The blue flags had given way to empty blue seats; the City players sank numbly to their haunches. Only the racket coming from the Liverpool fans in the south-east corner of the stadium seemed to register, a distant din in a deserted cathedral. Guardiola himself, of course, had long since departed the scene: sent to the stands at half-time, the director banished from the front row of his own production.

What happened in between was an object lesson in the key difference in football between intent and purpose, between speed and haste. The temptation, naturally, will be to attribute City’s Champions League exit, and the five goals they conceded over the course of this tie, to some sort of essential moral failing, a weakness of the core, a feebleness of the spirit.

Perhaps there may even be something in that. But what ultimately undid City was their failure to judge the tempo of the game, once at Anfield last week, and once again here. There they opted for control, here chaos, and yet where Liverpool took their chances with the coldness of surgeons, City flapped around like sturgeons. All the momentum, all the emotional energy, all the vigour they had managed to generate by virtue of their stunning start, ultimately ebbed away in a fog of blocked shots and interminable offsides.

“This time we begin the game trailing by three goals!” Guardiola wrote in his programme notes before the game, and somehow you feel that only Pep could make this most forlorn of lost causes sound like a wonderful adventure. Yet for three-quarters of an hour, it was an adventure.

From the moment Gabriel Jesus tucked the ball away to give City an early lead, they believed. Guardiola allowed himself a pump of the first. Klopp’s face went a wan, greyish colour, his nose scrunched up like a paper ball, a man bleakly aware that the next 88 minutes would knock years off his life. City didn’t even bother with a huddle; they celebrated individually, and then sprinted back to their marks. There was work to be done.

Perhaps, in hindsight, City were just a tad too quick in those early moments, setting an unsustainable pace that would find them out later. Yet in those opening exchanges, City’s speed was thrilling and ruthless, moving the ball, demanding the ball, hunting the ball. Even the ball-boys – doubtless at Guardiola’s drilling – seemed to be turbo-charged, flinging the ball back into play like infielders at a Twenty20 game.

Mohamed Salah’s goal, 10 minutes into the second half, put the tie beyond City’s reach. But by then, City had already stopped playing the perfect game that Guardiola had demanded. Guardiola himself had made the first glaring error, getting himself sent to the stands after angrily haranguing the Spanish referee Antonio Mateu Lahoz at half-time. And you wonder whether City’s players, learning of their manager’s indiscretion, began to question their resolve at that point too, as if to wonder: if Pep can’t even keep his cool, what chance do the rest of us have?

What happens now, of course, is anyone’s guess. These three consecutive defeats may not be enough to derail what has already been a staggeringly successful season by any standard. But these three games have reacquainted City with their footballing mortality. This was a huge opportunity missed: Real Madrid have been made to look ordinary by at least half a dozen teams this season, Bayern Munich have regressed from the team that Guardiola made them, Roma have no great pedigree in this competition (despite their stunning win against Barcelona). This could – perhaps should – have been City’s year.

They will be back, of course, and as Premier League champions. It will be the 50th anniversary of their first ever tilt at the European Cup, when the great side of Lee, Bell and Summerbee came unstuck against Fenerbahce at the very first hurdle before claiming the Cup Winners’ Cup the following season. Now, again, the hope for City fans is that this side will return stronger for their chastening experience.

After all, any City fan will tell you that if something is worth doing, it’s worth doing the hard way. It’s striking to think just how many of the most iconic triumphs in City history, from Gillingham in 1999 to QPR in 2012, from Tottenham’s 3-0 half-time lead in 2004 to Bert Trautmann’s neck in 1956, have come in the face of severe adversity. This is a club that is somehow at its most comfortable, its most purposeful, when it is standing at the foot of the mountain looking up, rather than at the summit looking down. Now, once again, they find themselves at base camp, the grand design on hold for another year at least.