Hoping to take advantage at home in the first leg of the Europa League semi-final, the Hammers were shocked when Frankfurt went ahead after just one minute through Ansgar Knauff.
But it was the visitors who got the winner through Daichi Kamada after 54 minutes.
The Japanese midfielder tapped home after Djibril Sow's low shot was turned into his path.
David Moyes' men must now overturn the deficit in Germany next Thursday to reach the final.
Speaking after the game, Moyes questioned whether his team had enough quality to beat Frankfurt.
"Disappointing result but there's another game to play," Moyes said. "Hopefully we play better in the second-leg. We didn't show enough quality in the final third. We switched off for the goals.
"Tonight was the worst for two years as far as set pieces are concerned. It has been a really strong part of our game but tonight we were really weak. Maybe we don't quite have the quality at times for this level. We have showed it at times.
"We didn't start the first or second half so well. They scored within a minute, which was a terrible start. Sometimes the opposition makes it hard. Tonight our creative players did not do enough when we had opportunities."
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