Three major retailers yesterday posted sharply lower first-quarter profits, largely because of sluggish sales.

Federated Department Stores Inc., the fifth-largest general-merchandise retail chain, said it earned $29.1 milion (60 cents a share), down 28.5 percent from $40.7 million (84 cents) in the 1981 quarter. Sales rose 7 percent to $1.62 billion from $1.5 billion.

Federated officials blamed the steep profits decline on the troubled economy and inclement weather, and noted that the earnings were being compared with those for a period that "was by far the best in our history."

Cincinnati-based Federated's stores include Bloomingdale's in New York and the Washington area and Filene's in Boston.

May Department Stores Co. of St. Louis, parent of the Hecht Co. of Washington and Baltimore, said that profits fell 29 percent to $11.5 million (40 cents a share) from $16.3 million (56 cents) for the same period last year. Sales came to $734.4 million, an increase of 3.7 percent from $708.2 million a year earlier.

Allied Stores Corp., a New York chain that owns Jordan Marsh stores in New England and Florida and the Bon Marche, said first-quarter profits tumbled 81 percent to $2.369 million (12 cents a share) from $12.599 million (63 cents), although revenues increased 28 percent to $669.733 million from $523.652 million.

Allied said the purchase of Garfinckel, Brooks Brothers, Miller & Rhoads Inc. of Washington in September 1981 hurt profits in the 1982 first quarter because interest costs associated with the acquisition exceeded the earnings contribution from the Garfinckel operation.