The sides will meet in the last 16 of Europe's premier club competition, with the first leg taking place at the Petrovsky Stadium on February 18.
Watzke feels his side's visit to Shakhtar Donetsk at the corresponding stage last season will serve as good preparation for their next challenge.
"I can live with this draw, but Zenit do have a host of quality players such as Hulk and others. It's not the shortest trip for us, but we will manage," he explained.
"It's a good omen for us to play in St Petersburg. We had a long journey last year in the first knockout round when we played Shakhtar Donetsk. It was cold there as well and we prevailed."
Sporting director Michael Zorc added that he was simply relieved not to have drawn Manchester City in the first knockout stage. Manuel Pellegrini's side were ultimately paired with Barcelona.
"It may be a small advantage that we play away first," Zorc explained.
"We do not yet know how the weather will be there at the end of February. But honestly I'm glad we have not pulled Manchester City as an opponent in the second round."
