With joking references to his failure to achieve the presidency and to the trials, tribulations and sometimes the boredom of the last two years. Vice President Rockefeller said his political goodbye yesterday.

"For me, these past two unusual years, in all candor, cannot be said to have sorely tried either my talents or my stamina," Rockefeller said in his final address to the Senate.

"But out of this experience, I bequeath to my successor two helpful mottos of this office of high calling: first, 'They also serve who merely sit and wait;' and second, 'Wait and want not.'"

The remarks prompted laughter from the Senate floor, which was occupied yesterday mostly by Republicans, who fill only 38 of the chamber's 100 seats. Under the Constitution, the Vice President is the presiding officer of the Senate.

For the most part, the senators present were attentive to Rockefeller's remarks. They listened to the Vice President tell them he really did not want the office, which he assumed Dec. 19, 1974. They also listened to him say he took the job only because the country was in a "constitutional crisis" precipitated by the Watergate scandal.

Rockefeller officially will leave office at noon Thursday, when the mantle of the vice presidency is handed to Vice President-elect Walter F. Mondale, Rockefeller said yesterday that, despite the problems and frustrations of his tenure, he is leaving office with "the profound satisfaction that our country has returned secure to its regular elective procedures of representative government."

Rockefeiler concluded his brief speech - it lasted about eight minutes - with a mixture of pessimism and optimism.

"Clearly, tomorrow belongs to no one," he said. "Free peoples can claim no prior lien . . . These are the times that try the very soul of America . . ."

But, fear not, he said. "An America true to its principles is not only a beacon light for liberty, but the surest promise of freedom for mankind.

"And let me say again, as I did on the night I assumed this office, there is nothing wrong with America that Americans cannot right," he said.

At that, he received a standing ovation. Afterwards, Rockefeller was obliged to stand at the Senate rostrum for nearly an hour, accepting the voluminous praise of his colleagues.

First was Sen. Robert C. Byrd (D-W. Va.), the new Senate majority leader. "Nelson Rockefeller has shares his considerable talents in a way that has given genuine stability to the county at a time when the stability was greatly needed," Byrd said. "Vice President Rockefeller has had his disappointments . . . But every defeat has been a new challenge for him." Byrd added.

Byrd was followed by Sen. Howard H. Baker Jr. (R-Tenn.), the new Senate Minority Leader, who said that Rockefeller was "truly a leader of the Senate and an example for all of us."