Farke's side edged a tense opening-day contest 1-0 against Oliver Glasner's Nottingham Forest, with Stach's late set-piece the only moment of real quality in a game short on clear chances.
Glasner, taking his first game in charge of Forest, told BBC Match of the Day the outcome was close to what he had anticipated.
"Well, it was the game I expected. The one situation that will decide and one set-piece will decide. It was a game with very rare chances. Really disappointed, but this is what we have to expect today. At the end, after the throw-in, then two mistakes, a free-kick and anything can happen. We all know how well Stach takes free-kicks."
Asked about his defence, the Austrian saw encouraging signs despite the result.
"This was positive. I just think we had a few situations when we played quick and we created some half chances. Together for a few weeks, but we are very stable. Still a lot of work to do." On transfer business, he added: "No, to be honest, I didn't talk to anyone today. We wanted to start with a win. Now we have to deal with a defeat at home. We will face Leeds again here, and we can show we can learn from this game."
The two sides meet again at the City Ground in the Carabao Cup this week.
Leeds United captain Ethan Ampadu, speaking to Final Score, said a hard-fought opening away win was exactly what the squad had targeted.
"We've been working the last six, seven weeks to make sure we get off to the best start. We can't complain with a 1-0 away from home. We knew it was going to be a difficult place to come."
He praised the impact of debutants James Trafford and Harry Wilson.
"From the very first minute they walked in the building they have shown their quality. They have shown why they have been brought in to try and help us get to the next level. Harry Wilson fits in very well with everyone and I think the fans will enjoy him as well." Of the club's ambitions, he added: "We know our targets and goals, we want to be a Premier League club next season."
Farke, speaking to the media after full time, said the win capped an encouraging build-up.
"I am very happy. It couldn't be a better way to start the season. Also, a first clean sheet under our belt and several new signings on the pitch. I think it was a game of different periods. Both teams defended well. So out of the game, out of open play, there were not too many situations but the transition moments and, of course, the set pieces were always dangerous."
The German credited his side's defending and Stach's decisive strike.
"You always had to be spot on. I think the reason that we won this game was that we defended in the end each of the situations really, really well, and on the other hand, Anton Stach converted one set piece situation also with a good strike and with a decisive goal."
Farke handed a debut in goal to club-record signing James Trafford following his summer move from Manchester City, and was pleased with what he saw.
"He has this natural aura of confidence and calmness around him and this is exactly what we wanted. He played, of course, also a decisive part and if we return back to the dressing room with a clean sheet, then the goalkeeper was always excellent!"