Tottenham, and especially Antonio Conte, won't see the 1-0 first leg deficit as an insurmountable one, but they were disappointing in going down to a defeat at the San Siro.
Brahim Diaz, the former Manchester City youngster, bundled home the ball in just the seventh minute for what turned out to be the only goal of the game, with the Spaniard reacting after Fraser Forster had brilliantly kept out his first effort.
Spurs struggled to create much throughout the night, and could have ended up losing by more goals but for missed headed chances from Charles De Ketelaere and Malick Thiaw.
Here are game's main talking points.
1. Rafael Leao takes just one minute to make his mark
Rafael Leao is fun, isn't he?
Anyone who has watched him in Serie A or saw him at the World Cup knows that of course, with the Portuguese one of the more exciting talents in a national side who are surely now desperate to move on from the days of Cristiano Ronaldo.
Leao will have a large part to play in that evolution, and while it would be preferable to see him scoring more goals and being more consistent, you often can't stop watching him.
Emerson Royal certainly couldn't anyway, with the Brazilian in the firing line almost from the off as Leao made an immediate beeline for him.
Royal isn't exactly known for his crisp, clean tackling, and it was all he could do to clumsily upend the forward.
Leao - who at one point in the second half inexplicably upended himself, almost confirming his Jekyll and Hyde nature - had made an all-action start, and it set the tone for a bright beginning from the hosts.
2. Too slow Tottenham
Whether it was because Leao livened them up or not, Milan looked determined to make their presence felt early on.
They were helped by a lacklustre Spurs though.
It was far too easy for Theo Hernandez to burst through the challenge of Cristian Romero, and then Eric Dier just stood off him as he stared down the whites of Forster's eyes. It was all so passive.
What followed was harsh on the stand-in goalkeeper after he blocked Hernandez's effort and then brilliantly saved the first Diaz follow-up, with the second almost ushered over the line.
3. Oliver Skipp and Pape Sarr step up
If you'd have told Antonio Conte before the start of the season that this was the Champions League last-16 tie he'd be facing, he'd have gone through a lot of midfields before he said his preferable selection would be Oliver Skipp and Pape Sarr.
But after early wobbles the pair did well.
Thrown together in the absences of Rodrigo Bentancur, Yves Bissouma and Pierre-Emile Hojbjerg, the 22-year-old Skipp and Sarr, 20, weren't overawed by the grand settings, and although their quality on the ball could be questioned their effort and endeavour could not.
Indeed, it was the young pair who laid the platform for their side to work their way into the game.
4. Rash Romero risks becoming reckless
He'd been too timid for that Diaz goal so perhaps it is a bit too easy to pick on Romero for being headstrong, but there is a happy medium.
The Argentinean picked up his sixth booking in his last five Tottenham appearances early in the second half when he lunged at a darting Sandro Tonali. It wasn't anything more than a yellow, but the distance he launched himself from did give the referee a decision to make.
He's a fine defender, and a player that fans are sure to love when he plays for their team, but at times Romero can look a bit like a liability too.
With Eric Dier now banned for the second leg after his own yellow card he's going to need to stand up and be counted when the Italians head to north London in three weeks.
Just standing up more often would be encouraged.
5. Tottenham's creative differences
This won't be news to Spurs fans, but the lack of creativity in this Conte system really is quite stifling.
Whereas football fans in the wider world might wonder why Son Heung-min hasn't quite hit the heights during this campaign it is simply because he's not in the right system for it. Indeed, the fact that Harry Kane keeps scoring so many goals in it is a testament to his outstanding quality.
There's not a lot behind them though, or indeed out wide in the shape of a left wing-back who is too old and a right wing-back who is too erratic.
Dejan Kulusevski suffers in this system too, and with the three centre-backs hardly convincing and two young central midfielders given something of a free pass, you have to end up asking: just who is this benefitting?
A 1-0 away defeat isn't the end of the world of course, especially without the away goals rule any more, but it is all fairly sterile.
