The Magpies were at one stage heading for the knockout stage as they led 1-0 at half time through Joelinton's wonder goal.
But they have followed Manchester United in being dumped out of Europe altogether having finished bottom of Group F.
Eddie Howe's men went into the game knowing they had to beat the Serie A giants and hope that Paris Saint-Germain failed to triumph at Borussia Dortmund.
Dortmund did their job by holding PSG to a 1-1 draw, but the Toon outfit conceded two second-half goals against the run of play.
Joelinton sent the home fans into a frenzy when he scored a stunning half-volley into the top left corner just after the half-hour mark.
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Milan looked dead and buried going into the break, but ex-Chelsea duo Olivier Giroud and Christian Pulisic combined for their equaliser in the 59th minute.
A glorious pass from Giroud found the American winger from a few yards out, who tucked home under Martin Dubravka.
Bruno Guimares was then denied by Milan goalkeeper Mike Maignan with a fantastic strike which would have lifted Newcastle into second spot.
And after Rafael Leao spurned a great chance, substitute Samuel Chukwueze curled an exquisite strike, with his first touch of the game, into the far corner in the 84th minute.
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The hosts desperately pressed for a late equaliser of their own to secure a Europa League spot, but they failed to create anything of note.
And it was Milan that came the closest to scoring another, with Fikayo Tomori hitting the post in added time.
The defeat means that Newcastle finished fourth after six matches - picking up just five points having won just once.
It is now three losses in a row for the Newcastle following their setbacks against Everton and Tottenham in the Premier League.
In the end, their controversial draw away at PSG last time out has proved costly in their quest for European glory.
But Howe can be proud of his team's displays in the club's first Champions League campaign since the 2002/03 season.