"To replace Lahm and Alonso is impossible, because of the quality, the experience, the personality," Ancelotti said.
"But we have other players who can continue this way like [Manuel] Neuer, [Thomas] Muller, [David] Alaba.
"We have a squad with fantastic experienced player and strong personalities.
"To replace them with their specific technical quality is really difficult; to find a right back like Lahm and a midfielder like Alonso."
As well as placing a burden of responsibility on the likes of Neuer, Muller and Alaba, one player who has been tipped to step up is Kimmich.
The 22-year-old, who joined the Bundesliga giants from Stuttgart in 2015, has scored five goals in 24 league appearances this season.
"As a right back the natural substitute [to Lahm] is Kimmich," said Ancelotti.
"He has a really big future here and I am sure he'll be a fantastic right back."
Bayern host Freiburg at the Allianz Arena on Saturday, May 20.