In a game that fizzed an crackled from the first second to the last, City fans were on an emotional roller-coaster as the tie ebbed one way then another.
And leading 4-3 in added time, Raheem Sterling was denied a winning goal by VAR.
The Blues could not have done anymore, but technology denied a richly-deserved goal that would have sent City into the semi-finals.
The game could hardly have started in more dramatic fashion.
City got off to a dream start and were ahead after just five minutes as Kevin De Bruyne found Sterling on the left and the England winger cut inside his marker before curling a beautiful shot past Hugo Lloris to send the Etihad wild.
What followed was not scripted as Spurs hit back not just with one goal, but two inside three minutes to leave the home fans stunned.
On each occasion Heung-Min Son was the scorer as he first latched on to a rare Aymeric Laporte to fire a shot that wrong-footed Ederson, and then as City were caught on the break, he fired a rising shot from 15 yards to put Spurs 2-1 ahead.
Suddenly, the North Londoners held all the aces – two goals ahead on aggregate and two precious away goals in the bag with just 11 minutes played.
But City hit back immediately as the breathless encounter continued.
Spurs were caught napping as the Blues poured forward and Sergio Aguero worked its way to Bernardo, the Portuguese hit a low shot that deflected past Lloris to make it 2-2 – incredible stuff and just the tonic the still shell-shocked Blues needed.
Four goals in the opening 12 minutes – the game was shaping up to be a Champions League classic.
Now it was Spurs who were wobbling and in only the 21st minute of the game, we had the evening’s fifth goal.
Bernardo held the ball long enough to feed De Bruyne who had enough time and space to play a low cross to the far post where Sterling was waiting to tap home City’s third and his 23rd of the season.
Rarely has such a high-profile game swung one way then another in such a short space of time, but the Blues had worked their way back into the tie when most other teams would have crumbled.
Another goal was still needed, however, though it would not arrive before the break with City taking a 3-2 lead into the second-half.
City could – and probably should – have had a fourth within five minutes of the re-start as a well worked move, orchestrated by Ilkay Gundogan saw David Silva cross low and Sterling hit his shot straight at Lloris with Bernardo unable to slide home the rebound.
Then Lloris pulled off a wonder save as De Bruyne fizzed a shot in from 15 yards just three minutes later as the Blues looked to go ahead in the tie on aggregate for the first time.
Just before the hour-mark Spurs reminded everyone of their danger when a lightning-fast break almost saw Son break free, only for a magnificent last-ditch tackle from Vincent Kompany to stop the South Korean in his tracks.
De Bruyne burst through the middle, waited for the right moment before sliding a pass to Aguero who thumped an unstoppable shot past Lloris to finally put the Blues in the lead overall and 4-2 upon the night.
But the drama was far from over and from a corner, Spurs regained an aggregate lead when Fernando Llorente bundled home from close range and despite a lengthy VAR check, the referee gave the goal.
City had 15 minutes to save their Champions League campaign.
It had been an incredible effort by the Blues and there was still time.
Sub Leroy Sane nodded a deep cross into Gundogan's path with five minutes remaining but the German's effort from close range needed a subtler touch.
Then, deep into injury time, the most cruel finish imaginable as Aguero squared to Sterling who slid the ball home to seemingly put City through - only for VAR to rule the goal offside.
City didn't deserve to lose this game, but somehow, over two legs, we have.
Star man: Kevin De Bruyne
Superb again from the Belgian who did everything in his power to steer City through
"It’s tough. It’s cruel but we have to accept it. It was a nice game for everyone. Second half we did everything. We scored the goals we needed but congratulations to Tottenham and all the best for the semi-finals.
"I support VAR. But maybe to see the goal from Llorente’s handball. I am fine for fair football and fair decisions. The referee must be helped. In the future and the present, it will be fair and that’s all.
"I don’t know (if Raheem's goal was offside). The referee decide it’s offside, so ok. We miss a penalty in the first leg, created an incredible amount of chances today. I am so proud, especially of the fans for the reaction and the incredible reaction. I never saw the stadium like today. We are sad for all of them but they know we have everything but football is unpredictable and unfortunately we are not in the next stage,"
What it means
City are out of the Champions League for this season and must now re-focus on the Premier League and FA Cup.
The Blues are back in action against Spurs on Saturday in the Premier League, followed by the Manchester derby at Old Trafford.