The 54-year-old says the club are working round the clock to find a replacement for the Poland international following confirmation he will join Bayern Munich next summer
The Bavarians announced on Saturday that the forward would join the club on a five-year deal once his contract with BVB expires this summer.
Watzke, reacting to the news of Lewandowski's departure, said he was fully expecting the announcement and the club is now committed to identifying a suitable replacement.
"This is not surprising, it is a completely normal process," the 54-year-old was quoted in Bild am Sonntag.
"In recent weeks it had been clear that it would come to this. Our sports director Michael Zorc is working flat out to find an alternative."
Lewandowski, who is currently joint top scorer in the Bundesliga with 11 goals so far this season, had long been anticipated to move to the Allianz Arena and Watzke stressed that he had no concerns over the 25-year-old's commitment to the club for the remainder of the campaign.
"Between us and Robert there is no problem," Watzke stressed.
"I have not the slightest doubt that there will be any changes to his strong performances."
Bayern sit at the top of the table with 44 points, 12 ahead of fourth-placed Dortmund.