"We weren't 100 percent ready from the first second, perhaps we were too intent on scoring," said Dortmund goalkeeper Burki after Wednesday's defeat with the Germans failing to overturn their 3-2 first-leg defeat.
The Germans bowed out leaving Monaco to join Real Madrid, Juventus and Atletico Madrid in Friday's draw for the Champions League's semi-finals after winning their quarter-final 6-3 on aggregate against Dortmund.
The Germans were rocked by last week's attack when three explosive blasts hit the team coach on the way to the first-leg match leaving defender Marc Bartra needing surgery for a broken wrist.
Police are still hunting the culprits.
The home leg was eventually played last Wednesday, but the shell-shocked Borussia players later complained they were traumatised by the events of the previous 24 hours.
In Monaco, French police held the Dortmund team bus up by around 15 minutes for security reasons, which German coach Thomas Tuchel said unsettled his players.
"After what happened to us, there is hardly a worse feeling than sitting together again on a bus which isn't moving. It was an oppressive feeling," he added.
Former Germany international Marcell Jansen said the trauma of last week was plain to see and had hamstrung Dortmund's performance in Monaco.
"The players are still feeling the effects, one can see that clearly," said Sky pundit Jansen.
"That wasn't the Dortmund we know. That was a team who wanted to do everything, but just couldn't do it."
Dortmund's plight in Monaco was not helped by Tuchel's decision to play Erik Durm, who has just returned from injury, on the right wing, which proved to be a disaster.
The Germany international was dragged off after only 26 minutes as Monaco had attacked freely down his channel and raced into a 2-0 lead through goals by Kylian Mbappe and Radamel Falcao.
Germany winger Marco Reus pulled a goal back for Dortmund after the break, but Valere Germain came off the bench to score Monaco's late third to seal the win.
"The early goals unsettled us," admitted midfielder Julian Weigl.
"We said at the half-time break that we could still score three in the second-half, but their third goal was a knock-out (punch)."
Tuchel later took responsibility for starting Durm, but the damage was already done.
Dortmund's director of sport Michael Zorc said it will take time for the team to get over the bomb blasts with a German Cup semi-final still to play next week against Bayern Munich.
"The explosion before the first leg won't be processed in just a week or two," he said.
"But that doesn't help us, we're still in a three-day rhythm and have to face the challenges."