Leipzig were without a chance as City forward Erling Haaland (22) scored five goals en route to an 8-1 aggregate victory in their Champions League last 16 tie.
But with the battle for a spot in the competition next season raging in the Bundesliga, Leipzig have little time to waste on self-pity, Rose said.
"I've been in this business long enough. It is an extremely bitter defeat. No one needed this but it happens," said Rose, who took over in September and turned their season around.
"It is now all about reacting appropriately. This heavy defeat can trigger things," he added. "To learn the lessons and become motivated on the next task because the Champions League is over for us."
Following a bad start to the Bundesliga season Leipzig have bounced back in recent months and are in third place on 45 points, seven behind leaders Bayern Munich.
But their top four finish that leads to the Champions League group stage next season is far from secure with Union Berlin and Freiburg also on 45 and Eintracht Frankfurt on 40.
Leipzig have also won just three of their last six league games to lose some ground in the title race. They next travel to struggling VfL Bochum on Saturday.
"Obviously the lads are gutted but we will continue on Saturday. We will have to work through a few things but on Saturday we are back in the Bundesliga. We have goals there that we want to tackle," Rose said.
Holders Leipzig are also through to the German Cup quarter-finals where they face Borussia Dortmund next month.
"Saturday things continue and we will need new energy then. It is not important not to just focus on self-pity and criticism," Rose added.
"On Saturday we have a chance to do things better. That's the good thing about football. Within a short time you can do that. That's our task basically."
