With Dortmund and Paris Saint-Germain cruising in Germany, a win at home against Milan would have been enough for Newcastle to advance.
They also took the lead after just over half an hour through a giant shot by Joelinton.
But with the hour played, Christian Pulisic made sure that the dream of the CL playoffs was extinguished at St. James' Park.
Shortly afterwards, Alexander Isak was substituted in favour of Anthony Gordon, but he was unable to find the net.
Instead, it was Milan who made it 2-1 through substitute Samuel Chukwueze.
Dortmund won the group ahead of PSG. Milan will continue to play in the second tournament, the Europa League play-offs, while Newcastle will have to focus on the league play in the Premier League.