Speaking at a security conference in Bratislava, Nuland also said it was important that people in the eastern Ukrainian regions of Donetsk and Luhansk had a chance to take part in a coming presidential vote.
Western nations are watching closely Ukraine's presidential ballot on May 25. EU foreign ministers hinted this week that any disruption of the elections could trigger new economic sanctions against Russia.
"You see us working with our partners globally to try to set forward a very clear and well understandable deterrent," Nuland told the Globsec conference in the Slovak capital.
"Namely to say that if the May 25 elections don't go forward, if Russia continues to destabilize ... there will be further, deeper and, now, sectoral economic sanctions on Russia.
"And we do believe what we have already done is starting to bite," she added.
Pro-Russian rebels held referendums on Sunday in Donetsk and Luhansk which backed self-rule. The Ukrainian government, which sees Russia's hand behind the unrest in the east, denounced the votes as illegal.
After the vote rebel leaders in Donetsk and Luhansk called for their regions to become part of Russia, but this call has not been taken up by Moscow.
Nuland said voting in the presidential election would be impossible to organize in Crimea, annexed by Russia earlier this year.
It would be difficult in some areas of the east, but the Ukrainian government expected to be able to hold ballots in the "vast majority" of Donetsk and Luhansk regions.
"What's most important is that people of Donetsk and Luhansk get a chance to vote on May 25th and we'll see what they have to say," she said.
The United States and European Union started putting sanctions against Russia in place in March after Crimea's annexation in March, amid the worst East-West crisis since the 1991 collapse of the Soviet Union.
Ukrainian politicians and civil groups gathered on Wednesday for talks on how to quell the rebellion in the east, but Kiev's refusal to let separatists take part cast doubt on whether the meeting could defuse the crisis.