News of the 20-year-old German international signing for arch rivals Bayern came a day before Dortmund's first semi-final appearance in the competition in 15 years.
"I think there could have been a worse time to announce this - four hours before the game," Klopp told reporters with a wide grin on Tuesday.
"I talked with some of our players and there should be no doubt that we know how to deal with this situation. We will do everything, absolutely everything against Real and whoever wanted to distract us will not succeed."
Dortmund have every right to remain confident despite the news, having gone unbeaten in the entire competition so far and having also beaten the nine-time European champions in the group stage.
"It is clear that for us it is now a situation of 'Now, more than ever' because we can draw strength from this," said Klopp. "It is about how you deal with these knocks. We could even be stronger despite the news than if it had not happened.
"Obviously the timing is not convenient and everyone can speculate about why it came out now. But it is out now."
The Germans, with the highest average attendance per game in Europe, will be counting on a fiery 65,000 crowd to will them on as they attempt to make the final for the first time since winning the trophy in 1997.
But many in Dortmund have already vented their anger over Goetze's decision to trigger a release clause in his contract and the announcement coming so close before the game.
Some fans have called him a "traitor" on social media with reports putting the fee at 37 million euros.
Klopp appealed to Dortmund fans, who have seen Bayern take their Bundesliga title this term, to keep their eyes on the big prize rather than the Gotze transfer. It is unclear if he will play against Real.
"I think we all should use the time to process it and go into the game with the right attitude. The fans also have to put this into perspective," he remarked.
"We all should go and show that Dortmund are above everything else. Put personal disappointment aside. If someone cannot do it they should give their ticket to someone else.
"If they can then they should help create a sensational atmosphere because the team deserves to be supported and that is necessary if we are to have a chance against Real Madrid."
Dortmund clinched league titles in 2011 and 2012 as well as the German Cup last year, but Klopp said everyone at the club was hoping for another successful European run having made the semis in spectacular style after two late goals downed Malaga.
"If tomorrow someone cannot remember how much we have dreamed about this then they should not come," said Klopp. "I have been here a few years now and I know how much we have dreamed about this."
With the news conference over, Klopp got up but then returned to his seat for a final appeal to the club's fans.
"Let us have a special evening, a real Borussia evening. Leave all your
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