Omar Marmoush had put Eintracht in front from the spot after Jack MacKenzie fouled Eric Junior Dina Emimbe, but Dante Polvara equalised from a superb team move to the delight of the travelling Aberdeen contingent.

One of their number, however, was arrested after a pyrotechnic was thrown towards the home fans during the first half.

Aberdeen said they were "deeply disappointed by the actions of a small minority of supporters" and would fully co-operate with the authorities.

When Marmoush swept home from the spot in the 11th minute, it seemed Aberdeen could be in for a long night, but they were undaunted by the early concession, and hit back with a wonderful goal.

Bojan Miovski drove into space, released the marauding Nicky Devlin down the right, and the Aberdeen wing-back found the unmarked Polvara, who made no mistake from close range, lashing the ball into the roof of the net.

From there, Robson's side impressed. There was a stunning save from Kelle Roos to deny Paxton Aaronson, but Aberdeen went in at the break deservedly level.

Eintracht made changes at the interval, but continued to lack fluency in the opening stages of the second half. However, Koch lost Slobodan Rubezic from a Fares Chaibi corner and glanced a header into the far corner to restore the lead.

That enabled the German side to take more of a grip on proceedings, but there were still moments in the game for Aberdeen, and they could have snatched a point right at the death.

The ball found its way through to Ester Sokler at the back post, but the forward could not hit the target, volleying wide with the home defence helpless.

Player of the match - Nicky Devlin

He played out of his skin, covering every blade of grass and putting his body on the line, keeping Mario Gotze quiet before the German was substituted at the break

'Courageous' Aberdeen show signs of progress - analysis

Tyrone Smith, BBC Sport Scotland at the Deutsche Bank Park

Robson will have learned a lot about his Aberdeen players, as they showed bucket loads of character and courage.

Written off by virtually everyone going in to this game, they could have gone under when Frankfurt took the early lead - but they didn't, they stood up and were counted to a man, clearly rattling their illustrious hosts.

Yes, Frankfurt prevailed in the end, but given all the talk pre match about the supposed gulf between the sides, Aberdeen can certainly leave Germany with their heads held high.

Robson got his tactics spot on and will be hoping his side can take positives from this game forward as they seek to revive their stuttering domestic campaign over the coming weeks.

'We could have nicked a draw' - reaction

Aberdeen manager Barry Robson: "I think when you wear that Aberdeen jersey, and you're in Europe, you need to try to show that mentality, desire, fight, tactical know-how, and I thought they did all that in abundance.

"That is a terrific team we faced out there, full of top players. They worked extremely hard, stuck to the tactical plan, and in the last 10 minutes, we could have nicked a draw.

"I trust my players. They're a good bunch, and it's frustrating when it's a set-play and a penalty that's cost you. We're disappointed that we didn't come away with anything, but we need to move onto a big game on Sunday."

Eintracht Frankfurt coach Dino Toppmoller: "We knew it would be hard game, we know they fight for every ball, we know that they have also got good players up front.

"We expected they would play with two strikers, we didn't expect them to defend so deep. But, at the end of the day, we won the game, that is a good thing for us."

What's next?

Aberdeen return to domestic action against Ross County at home on Sunday (15:00 BST).

Their next Conference League outing is against HJK Helsinki at Pittodrie on 5 October, with the Finnish champions opening their Group G account with a 3-2 home win against Greek side PAOK.