Both moves are part of an effort to raise borrowing costs in the US for loans tied to cars, mortgages and business loans.
MSCI's broadest index of Asia-Pacific shares outside Japan handed back earlier gains and was down 0.1 percent after falling 0.7 percent the previous day.
Japan's Nikkei .N225 was effectively flat. Hong Kong's Hang Seng index slipped 0.1 percent to 28,110.33 and the Shanghai Composite in mainland China lost 0.2 percent to 3,357.81.
Before the Fed announced its decision, there were high expectations that monetary policymakers would drag interest rate expectations lower for 2017.
The median fed funds rate forecast for 2018 is still at the 2.1% from the most recent forecast. On Wednesday, the Fed left interest rates untouched.
The rate outlook also looms large for homebuilders, among the best performing industry group this year as interest rates have undershot expectations.
The greenback continued to advance against other higher-yielding currencies with the Australian and Canadian dollars, South Korean won and Indonesia's rupiah all well down.
The dollar fell less than 0.1 percent against a basket of major currencies and was down against the euro, the yen and sterling.
Currency markets had a muted reaction to Trump's latest comments on North Korea.
USA allies on Wednesday said that enforcing global sanctions on North Korea, and not mere dialogue, was key to getting Pyongyang to give up its nuclear weapons after President Donald Trump on Tuesday said he would "totally destroy" the country if threatened and mocked its leader as a "rocket man". The resolution of the stand-off over the United States debt ceiling in Congress has removed the final obstacle to the decision, which the Fed said would proceed at a fixed monthly level that can be adjusted as needed to be either faster or slower.
"That competes with Google and Microsoft (MSFT.O), and it's going to weigh on the entire tech space", said Michael O'Rourke, chief market strategist at JonesTrading in Greenwich, Connecticut.
The euro sank from around $1.20 to below $1.19 while the pound dropped below $1.35 in NY but the pair recovered some ground in Asia Thursday.
The Mexican peso pulled back slightly after dropping in response to a strong quake that struck central Mexico.
US data showing domestic home construction fell for a second straight month in August weighed on the dollar index earlier. The 10-year Treasury yield approached 2.30 percent.
Crude oil prices were little changed amid a wait-and-see mood as ministers from the Organisation of the Petroleum Exporting Countries, Russia and other producers meet later on Friday to discuss a possible extension of the 1.8 million barrels per day (bpd) of supply cuts to support prices. Brent crude, used to price worldwide oils, gained 16 cents to $55.64 a barrel in London.