Army Secretary Clifford L. Alexander yesterday rejected an appeal by the widow of Pvt. Eddie Slovik, the only American soldier executed for desertion since the Civil War, for a reversal of Slovik's conviction and payment of his GI insurance.

The Pentagon said Alexander affirmed a finding by the Army's Board for the Correction of Military Records that there is no reason to overturn Slovik's World War II conviction, and thus barred payment to his widow, Antoinette, of about $70,000 in life insurance.

Mrs. Slovik was informed of the decision about an hour before it was announced publicly. Her voice breaking over the telephone from a Washington hotel room, she called the decision "terrible, just terrible," and said, "A gross injustice has been done."

"Consider the pardons that were issued to Vietnam draft-dodgers and deserters, and Muhammad Ali - he refused to go in at all, yet he never was tried or sent to jail," said Mrs. Slovik, 62, who is impoverished and confined to a wheelchair.

[Ali was convicted of refusing induction into the Army and sentenced to five years in prison in 1967. In 1971, the Supreme Court unanimously reversed his conviction, ruling that the Selective Service erred in refusing to grant him conscientious-objector status.]

"Ex-President Nixon committed a gross injustice against the American people, and he was pardoned. He's not wanting for anything to eat, or a roof over his head," Mrs. Slovik said.

"I'm wanting. And I think a gross injustice has been done."

Robert DeFinis, a Landsdale, Pa., public relations man who has championed Mrs. Slovik's cause for three years, said she has notified the White House that she wants to appeal her case directly to President Carter.

A White House military affairs office spokesman said late yesterday afternoon he had received a message from DeFinnis but had not had a chance to return the call.

If her appeal to the White House fails, Mrs. Slovik still has several avenues to explore. She can ask the record board to reconsider its opinion, request her congressional representative to introduce a private relief bill, or appeal through the federal courts.

DeFinis said Mrs. Slovak would "likely" pursue an appeal through the courts first, but would eventually exhaust all possible means of obtaining the money she thinks the government owes her. "We're going to see this through right to the end," he said.

DeFinis said Mrs. Slovik had been living on a $25-per-month Social Security payment, which was raised to $100 per month when she recently turned 62. He added that he and Sloviks' orginal defense counsel, Maj. Edward P. Woods, have spent more than $150,000 in legal, travel and communications costs in Mrs. Slovik's behalf in the past three years.

Slovik was among 49 Army deserters sentenced to death during World War II, but was the only one executed. At the board's hearing in June, there was testimony that Slovik was shot as an example.

Reuter news agency reported yesterday that 142 American soldiers were executed during the war, but, except for Slovik, the executions were for other crimes, such as rape.

Slovik's case became familiar to thousands of Americans when William Bradford Huie wrote "The Execution of Private Slovik" in 1954. The book was made into a television special.

Slovik, a juvenile delinquent from a poor Polish family, was 24 when he was inducted into the Army in January, 1944.That August, his unit was shipped out to England, Paris, Belgium, and ultimately to the Sigfried Line in Luxembourg.

During that time, according to an Army memorandum, "occasional enemy action was encountered and up until the time of trial the company was engaged generally in fighting and campaigning in the invasion."

Slovik deserted on Aug. 25, according to testimony at this trial, and returned to his unit Oct. 4. He deserted again on Oct. 8, and returned the next day.

The board concluded that Slovik "deliberately took actions to avoid combat, apparently assuming that such actions would lead to his conviction by court-martial and would result in his being confined within the relative safety of the stockade."

A different picture of Slovik's motivation is painted in a note he wrote - with frequent misspellings - after his second desertion:

"I Pvt. Eddie D. Slovik No. 36896415 confess to the desertion of the United States Army. At the time of my desertion we were in Albuff in France.

"I come to Albuff as a replacement. They were shilling the town and we were told to dig in for the night. The flowing morning they were shilling us again. I was so scared nerves and trembling that at the time the other replacements moved out I couldn't move.

"I stayed their in mu fox hole till it was quite and I was able to move. I then walked in town. Not seeing any of our troops so I stayed over overnight in a French hospital.

"The next morning I turned myself over to the Canadian Provost Corp. After being with them six weeks I was turned over to American M. P. They turned me loose.

"I told my commanding officer my story. I said that if I had to go out their again I'd run away. He said their was nothing he could do so I ran away again AND ILL RUN AWAY AGAIN IF I HAVE TO GO OUT THEIR."

Slovik was executed Jan. 31, 1945.