Gotze will join Borussia's Bundesliga rivals in the summer with the announcement of the deal coming on the eve of the biggest game in the club's recent history.
The move has angered Dortmund's fans, coming as it does less than a year after the Germany international put pen to paper on a new contract until 2016 which appeared to put an end to speculation about his future.
However, Bayern have agreed to buy out his contract, activating a release clause to allow him to join them in July.
Until he switches allegiances, though, Klopp is convinced Gotze still has a bit role to play in his side's season, starting against the Spanish champions.
"If we deal with this properly, then Mario will help us reach our goals," said Klopp.
"The news is out now and we can get back to playing football. Everybody should have had enough time for this news to sink in before kick-off.
"We will do all we can to ensure that whoever it was who wanted to disturb our preparations for this game will be unsuccessful.
"We have all dreamed of this situation and will not let anything distract us from it. In fact, maybe such a blow will make us even stronger."
Dortmund will have to be at their strongest if they are to repeat their group stage heroics and maintain their unbeaten record in the Champions League this season, and against Real.
The Westphalians won 2-1 at home and only a late goal from Mesut Ozil denied them a win by the same scoreline in the Spanish capital.
Ozil will once again line up against many of his national team colleagues at the Westfalenstadion on Wednesday night, and he hopes it will be a case of third-time lucky, in more than one sense.
"I'm looking forward to playing against my team-mates from the Germany team. It's my third semi-final with Real Madrid and I hope to reach the final. We are going to give it our best on the pitch and try to fulfil our objectives," he said.
That objective for coach Jose Mourinho is to reach a second final in four years having made it to the last four for a record-equalling seventh time.
After losing out to Bayern Munich a year ago, he is also keen to avoid defeat to German opposition for the second year running, but says the tie, and the Champions League, is wide open.
"Four of the six teams everybody was expecting are in the semi-finals," he said. "It could have been (Manchester) United or Juventus, but no other team.
"I would say it is 25% for Dortmund and 25% for Real to win the title."