A lacklustre first leg led to a more energetic second in which Jarrod Bowen and Lucas Paqueta each failed to tuck home good opportunities before Michael Gregoritsch was in the right place at the right time to tuck home the winner 10 minutes from time.
The Hammers thought they had a penalty deep into injury time but the referee refused to overturn his original decision after looking at the pitchside monitor.
Here’s how David Moyes’s side rated in Germany...
Lukasz Fabianski 6
Backed to continue as the cup goalkeeper despite Areola’s excellent league form. Hardly worked all night but could only parry Sallai strike to Gregoritsch for Freiburg's goal.
Vladimir Coufal 6
Made a vital block on Sallai from six yards out to deny Freiburg the lead inside 30 seconds. Alert all night.
Konstantinos Mavropanos 7
Very solid defensively in a game that suited him, with few demands on him in possession. Hit the outside of the post with a header from Ward-Prowse corner.
Kurt Zouma 6
One hairy moment in the first half when almost involved in a mix-up with Paqueta, then went to sleep for Gregoritsch's winner.
Emerson 5
Given plenty to think about by the sparky Doan. Off injured midway through the second half - would be a big miss should it prove anything serious.
James Ward-Prowse 6
A European knockout debut for the Englishman and almost created the opener with a corner from which Mavropanos hit the post.
Edson Alvarez 6
Excellent in the middle of the park until a sloppy pass surrendered possession in lead up to Freiburg's winner.
Tomas Soucek 6
Needed to be a little more composed when rare chances to break opened up but another who played a key role in keeping this a cagey affair. The nuisance value in the box almost won a late penalty.
Mohammed Kudus 7
Made the best chance of the first half for Bowen with a clever cross, then the best of the second for Pauqeta with a similar ball.
Jarrod Bowen 6
Read More
Hold up play is improving all the time at centre-forward but missed a big chance when scuffing at the back post. Then saw a fine strike tipped around the post.
Lucas Paqueta 5
Was lining up the opener when denied by Doan’s superb intervention, then headed over when he should have done better from Kudus's cross. Sloppy. Booked.
Substitutes
Aaron Cresswell (Emerson 68’) 6
Almost made late chance for Bowen with fine cross. Perhaps could have tucked in to pick up Gregoritsch, with Zouma caught the wrong side.
Kalvin Phillips (Ward-Prowse 82’) N/A
Michail Antonio (Paqueta 90’) N/A
Unused: Areola, Anang, Ogbonna, Johnson, Casey, Earthy, Orford, Ings, Mubama