Milan hold off toothless Tottenham to reach Champions League quarters
A European elimination hot on the heels of an exit from the FA Cup means Spurs' 15-year wait to win a trophy will extend for at least another season.
Conte's return to the touchline failed to inspire a response from his side as Tottenham were toothless in attack and had to play the final 12 minutes a man down as Cristian Romero was sent off for two bookable offences.
"I'm really sorry for the fans, but we cannot invent the win or to hope for a miracle one day that a trophy goes into our training ground," said Conte.
"We have to build and have patience. I understand the fans don't have patience as for a long time Tottenham is not winning."
Victory over two legs takes Milan into the quarter-finals for the first time since 2012.
"We deserved this result, even though we could have scored more," said Milan striker Olivier Giroud.
"We showed quality, spirit, and we could have won tonight as well."
Animated Conte
Kick-off was delayed by 10 minutes after the later arrival of both sides due to traffic congestion, but it took far longer for the contest to get going.
Conte was back in charge after taking more time after the first leg to recover from gallbladder surgery.
The Italian was his usual animated self and was shown a yellow card by referee Clement Turpin for his protestations at a booking for Clement Lenglet.
However, his players lacked the same energy as Spurs failed to rise to the occasion.
Tottenham have now won just two of their last seven games, including defeat to second-tier Sheffield United in the FA Cup.
Conte's contract expires at the end of the season and he did little to quash speculation that he will leave at the end of the campaign.
"The situation is really clear. It is one year and three months since I became coach of Tottenham, I always said the same things," added Conte.
"We need time and patience because we don't have a solid foundation to be competitive to win in my opinion.
"At the moment the club knows very well my thoughts and I have a great relationship with my chairman, with (sporting director) Fabio Paratici, but it doesn't mean I don't tell them my vision.
"Now we have to finish the season. I'm happy to work in Tottenham but at the end we'll make a decision."
Only profligate finishing by Milan saved Spurs from another defeat on the night.
Brahim Diaz scored the only goal of the tie and his jinking run inside the Spurs box just lacked the finish as Fraser Forster's outstretched leg deflected the ball to safety.
Spurs at least forced Mike Maignan into a save 25 minutes from time as he tipped over Pierre-Emile Hojbjerg's strike.
Conte gambled by switching to a front four for the final 20 minutes with Richarlison joining Harry Kane, Dejan Kulusevski and Son Heung-min up front.
But Kane's only chance to save his side came deep in stoppage time when his header was well saved by Maignan.
By that point, Spurs were a man down due to Romero's indiscipline.
The Argentine saw red for the third time in his Spurs career after lunging in on Theo Hernandez.
At the other end Sandro Tonali wasted another glorious chance by going for goal himself with teammates in support before Divock Origi's effort came back off the inside of the post.
But it did not matter as the seven-time European champions held firm to end more than a decade of waiting to reach the last eight.