The dinar shed 0.2 percent against the euro, to trade at 119.48 at 1341 GMT, after the bank lowered its benchmark rate by 25 basis points to 3.5 percent after a slowing in Serbian inflation.
Across the region, monetary policy is diverging, with the European Central Bank not rushing to follow the example of the Fed's tightening.
Hungary's central bank (NBH) cut one of its rates and announced measures to boost liquidity in forint markets while in August the CNB became the first in the European Union since 2012 to raise rates.
The Czech data failed to lift the crown.
But some of the region's other currencies and government bonds rose, recovering from a fall triggered by US jobs data which has strengthened expectations for a December interest rate hike in the world's biggest economy.
Czech figures released on Monday showed a fall in unemployment to a record low in September and a higher-than-expected 5.8 percent annual rise in industrial output in August.
Annual inflation rose to 2.7 percent in September, the highest in five years. The CNB said the inflation figures were in line with its forecasts.
The crown eased a little further to 25.89 against the euro, after its sharp retreat on Friday following the US jobs data.
Last week, at 25.789, it touched its highest levels since the CNB removed a cap that had kept the crown weaker than 27 versus the euro for more than three years.
The forint and the zloty recovered from Friday's lows, and government bond yields in the region mostly fell after a jump on Friday.
The Polish central bank may need a small rate hike early next year, rate setter Lukasz Hardt told Reuters.
Most analysts predicted a hike only for the last quarter of 2018 in a recent Reuters poll.
The forint, trading at 312.09 against the euro, was off the 5-month low hit on Friday at 312.58.
The NBH kept markets awash in money, injecting further forint liquidity through its weekly fx swap tender.
In Romania, where the central bank is facing a liquidity squeeze in leu markets, the government rejected all bids at a tender to sell April 2024 treasury bonds.
Five of seven analysts in a Reuters poll projected that the bank would keep rates on hold at its last meeting this year on Nov. 7.