Derek McInnes, the Aberdeen manager, insisted his side's Europa League hopes had not been extinguished by an impressive Real Sociedad team in San Sebastian last night, but they face a Herculean task in the return leg on the evidence of how this match played out.

The Pittodrie side were utterly dominated by a Sociedad outfit who simply oozed the class one would expect to witness from a team that finished seventh in La Liga last season. The gulf in quality between the two teams was more of a gaping chasm.

While the eventual two-goal deficit may have been semi-respectable, that was more down to rusty finishing from the home side rather than anything else. Sociedad could and should have been well out of sight, with second half goals from David Zurutuza and Sergio Canales the least the Basques deserved.

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But the fact that Aberdeen are still in the tie has given McInnes cause for optimism with a packed Pittodrie set to host the second leg next week. He said: "We will never give the game up but the task does become more difficult. We know the importance of the away goal, but we have seen games where they can quickly turn. We will have tremendous support at Pittodrie on Thursday and it is not beyond us to certainly ask more questions of them.

"I think we have to try and learn from this result but there is no disgrace in losing 2-0 to Real Sociedad. They are a very good side but we are not used to losing games and we have got a lot of boys who are disappointed and frustrated.

"The good thing about it is [that] it is half-time and we have another opportunity to get a better result next week. We will see [an improved] performance next Thursday and you never know, even though we accept it will be difficult. It is disappointing for us because we worked to prepare for it and in the game. But the better team won and sometimes you have just got to put your hand up and say that.

"I am always confident in my team. I applaud the players for their effort. Domestically we will not be dominated like that. There are a lot of frustrated boys because we thought we could come here and get a result but we have to remind ourselves that it's only half-time in the tie."

Sociedad actually started sluggishly, but after a dull opening period, they went on to dictate the rest of the game. New £8m signing Alfred Finnbogason made his first appearance and he almost marked it with a debut goal when he arrowed a header wide. Xabi Prieto, the home side's captain, was next to go close with a 20-yard effort.

La Real now had a firm grip on proceedings and Aberdeen were fortunate to get away with what looked like a more than decent penalty shout when Willo Flood launched a clumsy challenge on Finnbogason in the box.

Then Markel Bergara fizzed a long-range effort just over, with Aberdeen well and truly on the ropes.

Finnbogason should have done better 10 minutes from half-time when he volleyed Chori Castro's headed knockdown over the bar under pressure from the Aberdeen captain Russell Anderson. The hosts missed an even bigger sitter a few minutes later when Ruben Pardo ballooned a shot over from just 10 yards out after Prieto's excellent cutback.

For all that Sociedad had a stranglehold on the match, it took them until the 50th minute to test Langfield, when Finnbogason tried a speculative effort from an acute angle.

But Aberdeen didn't heed the warning and the Spaniards took a deserved 53rd-minute lead. Josepa Zaldua nutmegged Hayes on the edge of the box and although Shay Logan blocked Finnbogason's shot from the subsequent cutback, he only succeeded in teeing up Zurutuza who scooped the ball high into the net from close range.

The goal only served to send the Spaniards moving through the gears and the back-heels and flicks in their play gave lie to a growing confidence. The introduction of Andrew Considine for the completely anonymous Peter Pawlett failed to stem the tide, though, and Bergara cracked a 65th-minute shot against the bar after Barry Robson lost possession, forcing a frank exchange of views among the beleaguered Aberdeen defence. Considine then carelessly gave the ball to sun Sergio Canales who tested Langfield with an angled drive.

The second goal was inevitable and it was substitute Canales who showed his class with a goal just three minutes after he came on. He thudded a low 25-yard effort that flew into Langfield's net with such force that it gave the veteran keeper no chance.

Inigo Martinez thumped a header against the underside of the bar as Sociedad tried to get a third goal that would have ended all hopes of a second-leg comeback, but after several more near misses, the home side were made to settle for their two-goal advantage.