Brandt left as a free agent this summer after his contract expired, while Adeyemi is on the verge of completing a move to Barcelona.
Speaking to Sky Sport after Dortmund won an in-house friendly 3-1, Kovac addressed the changes to his squad as pre-season gets under way.
"We're very relaxed. We're working hard," he said. "Next week the internationals who were eliminated at the last-16 stage onwards will arrive.
"So the group will suddenly change. We'll manage it, we're very relaxed and we'll find the right path."
Kovac confirmed that strengthening the attack remains a priority following the departures.
"Of course we're working on it. We've lost two front-line players. That's why we're looking around, but we won't be in a rush," he said.
On Adeyemi specifically, who is expected to complete a switch to Barcelona in a deal worth around €29m including add-ons, the Dortmund coach struck a warm tone.
"We said goodbye to him. We really wish him all the best for his future."
Adeyemi's departure will end a spell in which the Germany international scored 36 goals in 146 appearances since arriving from Red Bull Salzburg in 2022, while Brandt leaves having made more than 280 appearances for Dortmund since joining from Bayer Leverkusen in 2019, scoring 51 goals and providing 61 assists across all competitions.
With most of Borussia Dortmund's World Cup contingent yet to return to training, Kovac's squad remains in a state of flux heading into the new season, though the head coach's comments suggest the club are not planning to rush into the market simply to fill the gaps left behind.
Maximilian Beier, Julien Duranville and Felix Nmecha are among those expected to take on greater attacking responsibility in the meantime, with Kovac keen to give his existing options every chance to stake a claim before any fresh additions are made.
The club's pre-season programme continues over the coming weeks as Dortmund prepare for the return of their World Cup-involved players, who will link up with the rest of the squad once their international commitments have finished.