The rate of U.S. union membership fell slightly in 2014, continuing a trend that suggests the labor movement will have to step up efforts to rebound from its decades-long slide.

See: Public-sector workers are nearly six times as likely to be union members.

Figures released Friday by the Bureau of Labor Statistics said the combined rate of private- and public-sector union membership was 11.1% last year, down from 11.3% the prior year. Membership in the private sector fell to a rate of 6.6% in 2014, from 6.7%, while public-sector representation rose slightly to 35.7%, from 35.3%.

Unions managed to collectively add about 41,000 members in the private sector, led by industries such as construction and leisure and hospitality, but it wasn’t enough to keep pace with total private-sector employment, said John Schmitt, a senior economist at the left-leaning Center for Economic and Policy Research.

“The overall workforce is growing faster than the union workforce,” said Schmitt, who said unions gained members in part because of workers who got new jobs in unionized facilities.

An expanded version of this report appears at WSJ.com.