The top seeds and Superseries champions were beaten 21-14 19-21 19-21 in France by Danes Mathias Christiansen and Lena Grebak in La Roche-sur-Yon, France.
The husband-and-wife duo led in the third game, but faltered and failed to save the last of three match points.
"No more than we deserved this week unfortunately," Chris Adcock later tweeted. "Played very poor all week."
Rajiv Ouseph of England and Scotland's Kirsty Gilmour reached singles semi-finals, with fifth seed Ouseph beating Danish fourth seed Hans-Kristian Vittinghus 19-21 21-12 21-19, and second seed Gilmour beating Spain's Beatriz Corrales 21-19 22-20.
England's Marcus Ellis and Chris Langridge beat Scots Rob Blair and Adam Hall 21-19 21-13 to reach the men's doubles semi-finals.
Britons Chris and Gabby Adcock suffered a surprise mixed doubles quarter-final defeat at the European Championships.