The 29-year-old Ukraine midfielder is expected to join the Bundesliga club this year in a deal worth 14 million euros ($17.86 million).
"He is one of our top players but we'll have to do without him after July," Advocaat told Reuters on Thursday at Zenit's training camp in this Mediterranean resort.
"I'm used to losing key players by now, that's the price you pay for being successful," said the Dutchman who guided Zenit to UEFA Cup and European Super Cup glory last year.
"Hopefully we'll be able to get a worthy replacement for him and sign a big player over the summer."
Advocaat lost Russia playmaker Andrei Arshavin earlier this month when he joined Arsenal in a big-money move.
The Zenit boss said he was gunning for the Russian league title and another UEFA Cup trophy.
"I'm not going to say that one is more important than the other. With this club we try to win every competition we are playing," he said.
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