Mauricio Pochettino admitted his Tottenham side were lucky to beat Wycombe after Son Heung-min's stoppage-time winner completed an incredible 4-3 victory.
League Two Wycombe, who are 70 places below Tottenham in English football's hierarchy, led this most pulsating of FA Cup ties on two occasions before Dele Alli equalised in the 89th minute, and Son sealed the win in the seventh minute of added time.
Pochettino made nine changes to the Tottenham team which drew with Manchester City last Saturday, and they trailed 2-0 following a first-half brace by Wycombe captain Paul Hayes.
And while goals from Son, and then Vincent Janssen from the penalty spot levelled the tie, Spurs played the final 20 minutes with 10 men after Kieran Trippier landed awkwardly, and could not be replaced after Pochettino had already deployed all three of his substitutes.
Garry Thompson then appeared to have sealed a shock win when he scored Wycombe's third with only six minutes left.
"In that moment, I said it would be tough to score again," Pochettino said.
"You always believe and try to win and be a little bit lucky, and today we got a little bit lucky to get into the next round.
"That is football, and I am sure they are very sad now and disappointed, but we can do nothing. Today was for us, and maybe on another day it goes for them."
Wycombe, fifth in League Two, arrived at White Hart Lane on the back of a 16-game unbeaten run, and they showed no signs of being intimidated by their more illustrious opponents.
Indeed they could have opened the scoring inside 60 seconds when Hayes' header hit the crossbar. Hayes did get on the scoresheet with a fine left-footed volley midway through the first half before doubling Wycombe's lead from the penalty spot.
Their half-time lead was richly deserved, but Spurs fought back after the interval and Son's stoppage-time winner evoked wild scenes at White Hart Lane.
"It was difficult for me when I arrived in England to say the FA cup is magic, or the 'beauty of the FA Cup', but now I realise it is a special competition," the Argentinian added.
"It is the most special competition in the world because you cannot replicate the same passion and the same atmosphere on the pitch in Spain, France or Italy.
"All of that is produced by a small-sized club like Wycombe from League Two. They are exciting and they believed they could beat us here. That is the important thing and the FA Cup creates that feeling."
Wycombe will now turn their attentions to the rather less glamorous affair of travelling to Exeter on Tuesday night.
"The result is frustrating, and there are a couple of incidents in the game - the soft penalty and the winning goal seems to have come in overtime of overtime - but I don't want to go negative," Wanderers boss Gareth Ainsworth said.
"As a manager you cannot ask for any more from your players. They have done the whole town proud, me proud, and themselves proud.
"I was gutted at the end but the overriding emotion now is just how proud we are of what we have achieved and how far we have come as a club."