TRENTON, N.J. (AP) â¿¿ New Jersey lost nearly 12,000 jobs in October, most of them in the private sector, even as the unemployment rate inched down to 9.7 percent, the state Labor Department reported. The drop of one-tenth of a percentage point, from 9.8 percent in September, still left New Jersey's jobless rate well above the national figure â¿¿ which was 7.9 percent for October. The Christie administration cited as positive signs a 4,500 increase in construction jobs last month and the fact that New Jersey has now recorded two consecutive monthly drops in the jobless rate, from the high of 9.9 percent in August. It also said the long-term job trend remains positive. The leisure and hospitality industry was responsible for the biggest loss in October, with 9,700 fewer jobs. Most of those were seasonal, and the state said the shift was bigger than usual. With the damage caused by Superstorm Sandy at month's end, the industry is also expected to take a major hit in November. Superstorm Sandy has already caused a spike in the number of people seeking unemployment benefits. For the week ending Nov. 3, New Jersey saw an increase of 5,675 in claims, caused by temporary job losses in construction, hotels and restaurants and manufacturing, the U.S. Labor Department reported. Preliminary estimates show nonfarm employment in New Jersey shrank by 11,700 jobs in October â¿¿ 9,400 of them in the private sector. The state also reported that job losses in September were even greater than preliminary estimates showed. Based on more complete reporting from employers, the number of job losses that month was put at 2,700, instead of 1,200. Residents of eight New Jersey counties â¿¿ Atlantic, Cape May, Essex, Hudson, Middlesex, Monmouth, Ocean and Union â¿¿ may be eligible for federal disaster unemployment assistance. The program is for people who worked in the affected counties but can no longer do so as a direct result of Superstorm Sandy's damages. Self-employed people are also eligible. People who are unemployed because of the disaster should first file for unemployment online at http://www.njuifile.net . People left jobless by Sandy have until Dec. 3 to file a claim.