The 21-year-old stunned BVB by agreeing to move to the Allianz Arena after Bayern met the midfielder's €37 million release clause back in April.
But after guiding Dortmund to three straight wins in as many games at the start of the new Bundesliga season, Klopp insists he is more than over Gotze's departure.
The 46-year-old told reporters: "One can say that there is a chance the team will play even better.
"Mario's transfer has not had a negative impact on us. It would have been nice if it had not happened but from a sporting point of view, his loss is already irrelevant."
Klopp was allowed to reinvest the proceeds of that sale into reinforcing a squad that finished runners-up to Bayern in both the Bundesliga and the Champions League last term.
Henrikh Mkhitaryan was brought in from Shakhtar Donetsk as Gotze's replacement in a €27.5 million deal, while striker Pierre-Emerick Aubameyang arrived from Saint-Etienne for an undisclosed fee.
And Dortmund were successful in preventing the Bavarians from taking another of their star men, Robert Lewandowski, by insisting the Poland striker see out the remaining 12 months of his contract.
BVB travel to Eintracht Frankfurt on Sunday as they bid to make it four wins out of four in the league.