Trailing 2-1 from the first leg of this Intertoto Cup semi-final, Newcastle took the lead through James Milner before conceding sloppy goals on either side of half-time.
It meant they will not feature in one of the major European competitions for only the fourth time in 12 seasons and that will be a considerable setback to both their finances and manager Graeme Souness's ability to attract the players he wants.
His chairman Freddy Shepherd has never hidden his desire to be in Europe, but whether Souness is equally dismayed at last night's exit remains debatable. For him, the Premiership is the priority. Souness said: "We can now fully concentrate on the job in hand. Only in May will we find out if it is beneficial to have gone out of this competition. If you don't have a big squad, fewer games give you a better chance of success."
Any prospects of domestic success will be limited unless Newcastle can eradicate their defensive errors, although Souness was without players such as Craig Moore, Titus Bramble and Celestine Babayaro last night. However, he did hand debuts to Emre and Scott Parker and both made significant contributions.
But Deportivo are an experienced and talented team, who possessed enough quality to recover after Milner had put Newcastle ahead in the 39th minute following a cross from Amdy Faye and a miskick by Lee Bowyer.
Jorge Andrade equalised in the closing seconds of the first half after beating Robbie Elliott and Shay Given to the ball - and Elliott was even more culpable for their second goal three minutes into the second half.
The left-back presented the ball to Pedro Munitis, who rounded Given and exchanged passes with Diego Tristan before scoring the goal that left Newcastle with the task of scoring at least three times.
Souness refused to blame Elliott: "The second goal killed us. It can happen, but I would hate to think we'll give goals like that away during the season."
Alan Shearer, denied a farewell season in Europe, said: "We all make mistakes. If I had taken a great chance soon after their second goal and their keeper had not made a number of great saves, you never know what might have happened. It might have been a different story on another night.
"We need more bodies in and that is clear for anybody to see," Shearer added. "We didn't have enough bodies here - the chairman and manager are trying to rectify it, but it is something that really tells its own story."
Newcastle United (4-5-1): Given; Carr, Boumsong, Taylor, Elliott; Parker, Bowyer, Faye (Ameobi, 52), Emre (Brittain, 90), Milner (N'Zogbia, 71); Shearer. Substitutes not used: Harper (gk), Ramage, Chopra.
Deportivo La Coruña (4-4-2): Molina; Manel Pablo, Andrade, Romero, Capdevila; Scaloni, Sergio (Valeron, 73), Duscher, Ruben Castro (Juanma, 63); Munitis, Tristan (Luque, 55). Substitutes not used: Dani Mallo (gk), Victor, Acuna, De Guzman.
Referee: H Fleischer (Germany).
The road ahead in Europe
They play Bulgaria's CSKA Sofia in the Champions' League third qualifying round. CSKA beat Albania's Tirana 2-0 last night for a 4-0 aggregate win.
Anorthosis Famagusta are next. Trabzonspor beat the Cypriots 1-0 last night but lost 3-2 on aggregate.
* MANCHESTER UNITED
Debrecen are their next opponents after thrashing Hajduk Split 8-0 on aggregate but Ireland's Shelbourne went out last night, beaten 4-1 on aggregate by Steaua Bucharest.
Beaten by Deportivo, who play Marseilles in the Intertoto Cup final.Reuse content