The Whites secured their place in the third round of the EFL Cup with a 2-0 victory at the City Ground.
Second-half goals from Daniel James and Lukas Nmecha sealed the win and capped an impressive display.
“The start to the season was not too bad!” Farke told the media.
“Of course, first and foremost, it was important to go through to the next round.
“This is what you play for this round. We did this in a tough place. We had to wait pretty long for a clean sheet win here at Nottingham and then to do it twice within four days is remarkable.
“I am pretty sure they were also even more motivated, also a bit out for revenge today. But the level of performance was decisive today.
“I think today was no doubt that was a well-deserved win. We dominated the game, more or less, from the first to the last second. And I just have compliments for the boys for the win but also for the level of performance today.”