WASHINGTON, March 5 (Reuters) - At a glance, the rebound in job growth in the hard-hit U.S. hospitality sector in February highlighted the potential for COVID-19 vaccines and falling infection rates to restore a labor market hobbled by the pandemic. But the distance from the economy’s pre-pandemic employment levels remained massive, and the details of the Labor Department’s monthly jobs report on Friday showed that one of the key racial equity measures now watched by the Federal Reserve in its drive towards “inclusive” maximum employment had faltered. A broad index of labor market indicators, consolidating 22 sets of statistics using a method developed by Cornerstone Macro, improved slightly, edging towards the high-water mark for U.S. workers in the 1990s. But for President Joe Biden’s administration, the 379,000 jobs that were added last month still left the economy about 9.4 millions jobs short of its level in February 2020. “If you think today’s jobs report is ‘good enough,’ then know that at this pace ... it would take until April 2023 to get back to where we were,” Ron Klain, Biden’s chief of staff, said on Twitter. The Fed may be thinking along similar lines. In December it said monetary policy would not change until there has been “substantial further progress” towards restoring maximum employment and reaching its inflation goal. Some metrics have improved since then. But the U.S. central bank now views maximum employment through a broader lens than before, and its aspirations took a step backward as the unemployment rate for Blacks actually rose in February - widening the gulf between the white and Black jobless rates for the first time since August. In fact, Blacks were the only racial or ethnic group to see an employment decline. Education levels were another point of disparity. All of February’s job gains were among people with at least some college education. Those without lost ground. There were signs of traction, however, in an economy that forecasters feel will at some point begin to rocket ahead as the impact of vaccinations is felt and life returns to normal. The bulk of the job gains last month were in the leisure and hospitality industry hardest hit by the pandemic in 2020. Data from employee time management firm Homebase saw what the firm felt were signs of a spring thaw coming for restaurants and small businesses. Shift work across a variety of industries also rose in February, according to data from time management firm UKG, and the pace appeared to increase in the second half of the month. “The jobs recovery is poised to accelerate in the coming months,” said UKG Vice President Dave Gilbertson. “March, which marks one year since shutdowns began, will set the stage for the spring recovery outlook.”