After scores finished 1-1, Wednesday went onto to win the penalty shootout.
"Some people will make headlines out of this but they are still professional football players, it's not like we played against a youth team," said Farke.
"We rested a few players to the bench or not even in the squad and it's always a bit tricky when you have so many changes, especially for the team that tries to make the game,
"We have to take the criticsm and we are self-critical because we should have have put four or five chances to bed.
"It's not just annoying, you feel a bit embarrassed as a Premier League side but we've been involved so many games like this, especially in the cup, and the lower-league team can win. This was one of these days.
"We were the favourites and of course we wanted to go through to the next round, so the result hurts.
"I wouldn't say it was an unbelievable surprise because we are a newly-promoted side to the Premier League travelling to a Championship side, it's not like we have played the last 30 years in the Premier League. It wasn't going to be a walk in the park to have an away game at a Championship side.
"I think by all the statistics we were the better side but the only thing that matters is the goals and after 90 minutes they managed somehow to be equal on goals and they managed to be the better side in the penalty shoot-out. Congratulations to Sheffield Wednesday.
"They deserved to win the game."