But the Clarets were unable to find a leveller as City demonstrated a stubbornness that will serve them well if they can transfer it consistently to their league performances.
"My feeling is it could have a really positive influence on the league because it's good for the rhythm and confidence of the players who have not been so involved in recent weeks," said Farke.
"It's another great away win after a really top-class performance against Tottenham [in a 2-1 defeat on Wednesday] with an unlucky outcome, so we are heading totally in the right direction.
"We were able to bring this tight result over the line in a cool and composed manner. We never had the feeling there would be an equaliser, and that was because of our focus and discipline."