For an administration under fire for lacking gender and ethnic diversity in its top posts, the nominations President Obama unveiled Monday have quieted some amount of the criticism — but not much.

Obama’s choice of Sylvia Mathews Burwell to head the Office of Management and Budget and Gina McCarthy to direct the Environmental Protection Agency adds two women to the Cabinet, in addition to Interior Secretary nominee Sally Jewell.

Obama also tapped Massachusetts Institute of Technology Professor Ernest Moniz to oversee the Energy Department. Still, members of the Hispanic community are waiting for a high-profile appointment and becoming increasingly uneasy as the number of available slots are dwindling. The grandparents of Moniz hailed from the Azores in Portugal, but that does not fit the traditional definition of Hispanic or Latino.

“I’d like to think we are a big-tent community and would welcome anyone who wants to work with our community, but I think it’s a stretch to call Secretary-designate Moniz a major Hispanic announcement,” said Janet Murguia, president and CEO of the National Council of La Raza. “He doesn’t classify himself as Hispanic.”

Or, as Princeton sociology and international affairs Professor Miguel Centeno put it in an e-mail, when it comes to the category of Hispanic, “the term is completely a bureaucratic invention (as is the case with all such categories). Would he count according to the census? I am not sure — probably not. Would he count if he got refused a reservation at a restaurant because of his name? Then yes.”

The departure of minorities from the first-term Cabinet has been dramatic. Two of the Cabinet’s four African Americans and both of its Hispanic members have left or have announced that they are leaving. Only one of the two Asian Americans who served during the first Obama term remains.

The White House has only five Cabinet or Cabinet-level posts to fill — meaning only five more opportunities to boost diversity. The openings are at the departments of Commerce, Labor and Transportation and the Small Business Administration, as well as U.S. trade representative.

Murguia, who said that administration officials have privately assured Latino leaders that there will be two Hispanics named to the Cabinet, noted that Latinos represented 10 percent of the electorate in 2010, and that 71 percent of them supported Obama’s reelection.

“They’re working behind the scenes on this, but it feels like it’s time for these decisions to be made,” she said. “The fact is, Hispanics did turn out to vote in a major way and voted for Obama in a major way, and that needs to be recognized as they’re filling the Cabinet.”

But Robert Raben, who chairs the Hispanic National Bar’s endorsement committee, said he was pleased to see that the White House tapped Edith Ramirez on Friday to head the Federal Trade Commission.

“It’s an important, substantive agency,” Raben said, adding that while it is taking time, “I’m cautiously optimistic that when the president is finished with his appointments, there will be an impressive number of Latinos.”

Terry O’Neill, president of the National Organization for Women, said Monday’s appointments were “encouraging” but still fall short when it came to folks with high-level “day-to-day access” to the president.

“What concerns me is that he needs to be hearing from women half the time,” she said, adding that Obama has done better when it comes to his government-wide and judicial appointments. “The good news is this is not an individual who needs binders full of women. He knows where the women are.”