National Football League Commissioner Pete Rozelle yesterday criticized a public television documentary on the NFL in which a gambler claimed to have fixed 12 NFL games as a "disgraceful example of cheap sensationalism and checkbook journalism."

In a prepared statement issued from his New York office, Rozelle called the documentary--"An Unauthorized History of the NFL"--"chiefly a rehash of press clippings, gossip and rumor, some almost 25 years old."

On the program, broadcast Monday by WETA-TV-26, a former gambler named John Piazza claimed to have fixed four NFL games a year in 1968, 1969 and 1970 by bribing a coach, a quarterback and a defensive captain. Piazza, who was interviewed while in prison, was paid $10,000 for his participation in the program.

The documentary, part of a series called "Frontline," also outlined a history of the NFL's concerns with gambling, and it traced some alleged associations between players and NFL owners and gamblers and persons connected with organized crime. It also suggested that the late Carroll Rosenbloom, owner of the Los Angeles Rams, who died by drowning off the coast of Florida in 1979, may have, in fact, been murdered because of alleged gambling connections.

Rozelle was especially critical of the fact that there were no names or dates connected with the 12 games said to have been fixed. "Without these facts, every player and coach of the period this show cited, 1968-1970, is subject to suspicion," Rozelle said.

In Dallas, Tex Schramm, the Cowboys' president and general manager, was quoted by United Press International as saying the program was a "total fabrication. I just think it was a very amateurish, unjournalistic program," said Schramm. "If it is true that PBS had two tapes--one of them which used the names--then they had a journalistic responsibility to try to contact the people whose names they had. That is the duty of journalism. I doubt if any of the three neworks would have touched it." Federals Add to Staff

Dick Bielski will be the Washington Federals' offensive coordinator and Gene Stauber will handle the defensive line, the United States Football League club announced yesterday. They are the first assistants named to Coach Ray Jauch's staff.

Former Maryland athlete Bielski, 50, served on George Allen's Redskins staff between two extensive terms with the Baltimore Colts, beginning under Don Shula in 1964 and ending as receivers coach under Mike McCormack, 1977-81. He played tight end in the NFL for Philadelphia, Dallas and Baltimore.

Stauber, 61, spent the past five years assisting Jauch at Winnipeg of the Canadian Football League. He coached at seven major colleges in a 25-year span.