Last season's Bundesliga champions announced on Tuesday morning that the Germany international playmaker will join the Bavarian giants at the end of the season.
"I knew [about Gotze's move to Bayern] the day after the Malaga second leg," Klopp told reporters on Tuesday.
"So I had 24 hours to be happy about that result. Nobody needs to worry about our focus. If anything, it is sharper than ever.
"Gotze was a player [Pep] Guardiola wished to sign. He knows he owes a lot to the club, but I know he gave a lot back as well. Gotze wanted to work with an extraordinary coach. I cannot teach the 'tika-taka' ways of Guardiola."
Dortmund will host Madrid in the first leg of their semi-final tie on Wednesday.