Atletico Madrid clinched fourth place ahead of Villarreal, while Valencia secured sixth to also qualify for Europe.
Barcelona were crowned UEFA Champions League winners on Wednesday following a magnificent 2-0 victory over Manchester United.
Having already won the domestic double, Pep Guardiola decided to make changes for the final game of a historic campaign.
Deportivo La Coruna needed to beat Barca to stand any chance of finishing sixth and they made the perfect start as Rodolfo Bodipo fired them ahead after 31 minutes.
However, Samuel Eto'o grabbed a last-minute equaliser to ensure Barca did not end their season with three consecutive league defeats.
Deportivo would have missed out on the final Europa League spot anyway after Valencia beat Athletic Bilbao 2-0 at home.
David Villa opened the scoring after seven minutes and netted his second of the evening in the 90th minute to seal the three points.
Bilbao will join Valencia in the Europa League despite finishing in the bottom half of the Primera Division table, having lost to Barca in the Copa del Rey final.
Villarreal are the third side to make it into the inaugural Europa League, although they had hoped to qualify for the Champions League.
Atletico Madrid started the final round of games two points clear of Villarreal and maintained their advantage courtesy of a 3-0 victory over Almeria.
Sergio Aguero broke the deadlock in the 19th minute and Raul Garcia made it 2-0 before half-time.
Diego Forlan then added a third after the break as Atletico registered a sixth straight win.
Villarreal ended the season with a four-game unbeaten run following a 3-2 success at Real Mallorca.
Ruben Gracia's opener was cancelled out by Aritz Aduriz but Joseba Llorente put Villarreal back in front five minutes before half-time.
Llorente's second gave the visitors a two-goal cushion and it proved important as Pierre Webo netted late on for Mallorca.
Primera Liga round-up
La Liga round-up
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