Joel Piroe scored twice and Georginio Rutter one in a 3-0 win, Leeds' first at the notorious south London ground since 2012.
It was only his side's second Championship win this season and manager Farke viewed it as a character test passed.
"I've played here several times and I know it's an unbelievably tough place to come," said the former Norwich City manager. "I know as a club we've waited more than a decade to win here so you have to be spot on.
"In periods you have to show some steel and resilience because you can't avoid all these long ball and long throw-ins and corner kicks.
"You have to give your life in these moments and stay cool and mentally strong to wait for the moments when you can calm the game down and let your quality show.
"When I think about the first goal you can put it straight away into a book and sell it, it's so wonderful."
Rutter's goal was only his second for the club he joined for £35m in January, and he was not the only attacking player who could take confidence from his performance.
“Dan James had two assists, (fellow substitute) Jaidon Anthony had a good chance and I think it was quite close to a penalty,” said Farke.
"It's always good for the confidence of my offensive players when they score and the relationship between Rutter and Piroe was quite good. In the last game I got the feeling Joel was too deep in his positioning but today he was a bit more flexible in his positions and with the wingers more fluent."
Clinical Leeds only had three shots on target, but limited their hosts to the same.
"It was important our offensive players did their job and put pressure on the build-up," said Farke.
"The midfield centre was quite crucial and our Joe (Rodon) had to be there with many clearances, dealing with their aerial threat. There was a little cut under his eyebrow but he showed warrior mentality."
Ethan Ampadu will be assessed ahead of Wednesday's short trip to Hull City, but Djed Spence will definitely miss out.
"He (Ampadu) took a knock but he's a fighter so I hope it's just a bruise and he will be available," said Farke. "Djed has done his lateral ligaments, he will be out for several weeks. It seems like no surgery is needed but he we have to wait for further assessment.
"Liam (Cooper) is back in training. It was the first time back in full training on Thursday. I want him back as quick as possible with his quality, his experience and his influence on the dressing room but he was out for more than six weeks and just two training session was not enough."
Millwall manager Gary Rowett felt Leeds' star quality held sway.
"A 3-0 scoreline doesn't look a fair reflection of the effort the players put in,” he commented. “It's a tough league when a team like Leeds have the ability to bring on players like Dan James, Anthony, (Joe) Gelhardt.
"We forced lots of corners and moments around the box without creating obvious chances but I didn't think Leeds did either."