The West Yorkshire club took a 2-0 lead against West Ham in the quarters, only to concede two goals late in added time.
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Leeds managed to win it on penalties, qualifying for their first FA Cup semi-final since 1987, in which they will face Chelsea.
Speaking to BBC Sport after the game, Farke said: “We will be the underdog, that’s for sure.
“It’s a big name and a side full of top players. For that we are the underdog but we have written history.
“Nobody expected us to go though to the semi-final. And of course we are greedy to go to the next step.
“My focus now is on the Premier League. We are on such a good path and want to make sure we can celebrate there.”