The Canaries, who were ahead in the fourth-round tie for 50 minutes before being pegged back, found themselves on the wrong end of two big calls by referee Andy Madley.
Farke believes that his side could have won had Madley got the calls correct, but is now eager to move on ahead of next weekend's home league match against Derby County.
"First of all I'm very proud of my lads, of this performance, especially 48 hours after a high intensity derby win, but the guys are really disappointed and sad in the dressing room and it is like this today," he told reporters. "We all had this feeling that we totally deserved to be into the next round, to win this game, even after 90 minutes. Sometimes it is [like this] in football so you don't immediately earn what you totally deserved, and you have to accept it.
"I'm not the guy who claims for red cards but I think this situation was obvious because we were in a one-on-one situation to the goalkeeper and that is early 100% true and that is to the determining situation of the game, and the game is done and we're in the next round.
"If Elneny concedes the red card, I think obviously he should have seen the red card, then it's 11 against 10 and then they are not able to build so much pressure and there are not all these set pieces and then there is no 1-1. So that would be the determining situation too so to accept that situation is quite hard. It's really hard but it is how it is so sometimes you have to accept mistakes.
"Sometimes my players make mistakes, sometimes the opponents, sometimes the referee and I'm pretty sure the ref wants to show his best performance but I think in this decision he was totally [wrong]. It had to be. It's really annoying because I speak about the topic, small things are determining for the game, and this situation was not a small situation. It was an obvious situation. It's hard to accept but that is what we have to do tonight."