Labor Secretary William E. Brock, responding to criticism of President Reagan's rejection of trade protection for the shoe industry, announced a $5 million initial commitment yesterday to aid 2,300 workers expected to be laid off permanently by 1987 because of foreign imports.

"This administration has not ignored the plight of workers in the shoe industry," Brock said in announcing an aid program targeted at the 16 states that employ most of the nation's 110,000 remaining shoe workers.

He noted that the new funding is in addition to $2.8 million spent in the last 20 months to aid 3,000 dislocated shoemakers.

Reagan, whose rejection of import quotas or tariffs for the shoe industry Aug. 28 resulted in strong complaints from Congress and organized labor, had directed the Labor Department to draft a retraining program for unemployed workers.

The president said the cost to consumers of protectionist measures would far outweigh the benefit of protecting shoe-industry jobs, which pay an average of $14,000 a year.

Brock asked governors of shoe-producing states to participate in establishing retraining programs under the Job Training Partnership Act.

Major states employing shoe workers, according to the Bureau of Labor Statistics, are Missouri, with 15,200 shoe workers; Maine, 14,400; Tennessee, 10,500; Pennsylvania, 10,300; Massachusetts, 7,300; New York, 6,900, and New Hampshire, 6,400.

Union officials criticized the administration's action yesterday, saying the job-training program is too small and too late to provide substantial assistance.

"This administration has cut back substantially on all training and trade-impact funds, and this isn't going to accomplish very much," AFL-CIO spokesman Murray Seeger said. "$5 million doesn't go very far."

Previous job training for shoe workers has been ineffective because job opportunities are often limited nearby in many shoe-producing areas, said Arthur Gundersheim, assistant to the president of the Amalgamated Clothing and Textile Workers Union (ACTWU), which represents about 20,000 shoe workers.

Since 1979, about 22,000 shoe workers have been eligible for assistance under the Trade Adjustment Assistance program, which provides extended unemployment benefits and retraining to workers who lose jobs because of foreign trade, Gundersheim said.

Of those, according to ACTWU figures, fewer than 500 completed training programs and fewer than 250 obtained new jobs.

"This $5 million is a reasonable amount to start with, and we hope there will be a better record under this program," he said, "but these programs only work when there are real jobs available."