Gladbach suffered an embarrassing quarter-final defeat to third-tier side Arminia Bielefeld on Wednesday, losing 5-4 on penalties after the sides were level at 1-1 after extra time.
Raffael and Ibrahim Traore missed from the spot to ensure Arminia can look forward to a semi-final against Wolfsburg later this month.
Dortmund were also taken to extra time a day earlier, but a sublime long-range volley from Sebastian Kehl secured a 3-2 victory over Hoffenheim and Jurgen Klopp's men will face Bayern Munich in a mouth-watering semi-final at the Allianz Arena.
Gladbach's cup defeat was hard to take for Favre, but the Swiss coach has warned his players not to dwell on that setback as they prepare for Saturday's Bundesliga encounter at Borussia-Park.
He said: "I'm obviously disappointed to not be in the semi-finals. We wanted to get through to the next round but we knew before the game that it wouldn't be easy.
"We tried to control the game but Bielefeld defended well and that meant we didn't get many chances to score. We were lacking the right tempo and we didn't find the gaps.
"Overall, we didn't do enough to win the game. It's hard to stomach going out on penalties but we have to get over the result straight away."
Max Kruse echoed Favre's sentiments as Gladbach aim to gain revenge for a 1-0 defeat to Dortmund in November, which came courtesy of a comical Christoph Kramer own goal.
The striker said: "It's incredibly bitter to go out on penalties. But we only have ourselves to blame. We were unable to beat Arminia after 120 minutes and therefore didn't deserve to go through to the semi-finals.
"We were unable to play the ball around with tempo and didn't create enough goal scoring opportunities.
"We need to completely switch our focus towards the game against Dortmund and try to achieve our goals in the league."
