Jurgen Klopp's side came into the home second leg of their last 16 clash with a realistic chance of reaching the quarter-finals, following a 2-1 loss in Turin three weeks ago.
However, they were outclassed by a Juve side who triumphed 3-0 on the night to seal a resounding 5-1 aggregate success.
With 10th-placed Dortmund seemingly out of the reckoning for a top-four finish in the Bundesliga and a return to the Champions League, Klopp wants his players to pull together as they eye a strong finish to what has been a testing campaign.
"If you are not strong enough, then you can't mind going out of the Champions League," he said.
"We weren't strong enough in the Bundesliga either. We have other problems, there are some reasons why we don't have 60 points in the league.
"We have to learn how to handle situations. We're better, but not good enough yet.
"We are out, now we can concentrate on the Bundesliga. We are together, we win together, we lose together, that's not the problem.
"It's not our best moment, but it is life and we have to stay in the race."
Domestically, Dortmund have been in good form, and head into the clash at Hannover on a six-match unbeaten run - although the last two games in that sequence saw them draw blanks in 0-0 stalemates with Hamburg and Cologne.
Hannover, meanwhile, are yet to win since their return from the mid-season break, with just three points from their eight games following the resumption.
That sequence has piled the pressure on coach Tayfun Korkut, with suggestions in some quarters that his job in serious danger.
However, club president Martin Kind insists that Korkut has not been given an ultimatum, and the coach has received the backing of his players.
"He is, in my opinion, the right coach," said goalkeeper Ron-Robert Zieler.
"The coach prepares us week after week meticulously. He does a good job," added ex-Dortmund midfielder Leonardo Bittencourt.
With Hannover 13th in the table and just four points above the relegation play-off zone, victory over a hurting Dortmund would go a long way to easing the pressure on Korkut.
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