Leeds took a 2-0 lead in the first half only to nearly throw it all away as West Ham scored two goals in added time.
The West Yorkshire club managed to get the win on penalties, progressing to the semi-finals where they will face Chelsea.
Speaking to reporters after the game, Farke admitted he was proud of the achievement and is happy for the fans.
“I feel pretty humble in these moments, you can see in the eyes how much it means to them,” he said.
“Last semi-final was the 80s and this club has had difficult decades. We wanted to be back in the top flight, we’re on a good path to earn our right to stay there.
“But to be back on the big stage, FA Cup semi-final at Wembley, more than 30,000 will try to overtake the capital.
“How much it means to them, especially in strange times in our world, it means a lot to give them some joy and pride back.”