President Carter told the Democratic Party's platform committee yesterday that it has the power to unify the party, and only "a united Democratic Party" can win in November.

Carter pleaded repeatedly for party unity in a 75-page document sent to the platform committee, which yesterday began the final stage in its drafting of a document of Democratic principles for the 1980 campaign. Most of Carter's long statement was a hymn of praise for his own accomplishments, but the repeated references to the need for unity revealed the president's true concerns about November.

"Our nation cannot afford . . . the prospect of four years of regressive Republican policies," Carter told the committee. "But these are the policies we will have if the Democratic Party fails the current challenge and does not unite to defeat the Republicans . . . fThe choice is yours. The responsiblility is heavy, but I know that you can meet it."

There was no evidence yesterday that anti-Carter elements in the party were ready to defy Carter and try to split the platform committee. On the contrary, the signals sent out by the camp of Sen. Edward M. Kennedy at yesterday's meeting generally seemed conciliatory, though Kennedy campaign aides promised to argue vigorously for their man's positions when final drafting of the platform takes place.

For their part, Carter partisans seem determined to put a unified face on whatever the platform committee produces, provided it does not directly repudiate the president's policies. Judging by the presentation yesterday of Stuart E. Eizenstat, Carter's assistant for domestic affairs, Carter will accept almost and liberal Democratic proposals in the platform, provided he is allowed to phase them in at some indefinite time.

The only Kennedy proposals that Carter or his spokesmen explicity rejected yesterday were those recommending wage and price controls and gasoline rationing, a position articulated by Carter two weeks ago.Because pro-Carter delegates will have a clear majority on the final platform committee, there seems no likelihood that either of these could be adopted as party policy.

Paul Tulley, one of the senior officials of the Kennedy campaign, spent yesterday as an observer at the platform hearings, and said late in the day that the session represented "a pleasant enough start." Tulley expressed satisfaction with the committee's decisions early in the day to adopt some of the Kennedy camp's proposals for opening up the platform process.

The full committee adopted several changes in the proposed rules that will make it relatively easy for the Kennedy camp to bring up any proposal for a change in the platform and get a vote on it from the committee.

Carter's detailed presentation to the committee amounted to a statement in his own defense and an introduction to the points he will be making during the general election campaign. "Our party has not generally received the credit and recognition we deserve for the progess made since 1976 in meeting our nation's most serious problems," Carter said. He did not shy from compensating for the lack of credit he preceived.

According to Carter, his administration has restored the country's trust "in the integrity and honesty of our nation's leaders," saved Social Security from bankruptcy, preserved the environment advanced blacks and Hispanics into important jobs at unprecedented rates, cut the federal payroll and the budget, helped farmers and lower-paid workers, reorganized the government and expanded the social programs with which the Democrats traditionally have been identified.

"When my 1981 budget is compared with the last Republican budget," Carter said, "major funding increases in programs vital to the low-income and the disadvantaged are apparent." He cited: aid to education up 73 percent, Head Start program up 73 percent, handicapped education aid up 232 percent, youth employment programs up 300 percent. These figures are based on budget proposals, not congressional appropriations.

In a presentation of Sen. Kennedy's views, his issues director Peter Edelman, gave a ringing reassertion of traditional liberal verities, including calls from many new or strengthened federal programs. In the energy field, Edelman reiterated Kennedy's views, which closely follow the 1976 Democratic platform, and contradict Carter's which virtually ignore the '76 document.

Later, at a White House reception for committee members, President Carter said he is "extremely eager to see rifts healed." However, he said, there need be no "fear or consternation" if some disputes can't be settled in committee and must be put to the full national convention.

The committee yesterday approved a 15-member drafting subcommittee that will do the first serious work writing a platform. It includes these nine Carter supporters: Rep. Lindy Boggs (D-La.); Lt. Gov. Mario Cuomo of New York; Mayor Kenneth Gibson of Newark; Gwen Martin of the Communications Workers of America; Barbara Roberts Mason of the National Education Association; Ned McWherter, speaker of the Tennessee legislature; Marge Price of the Colorado legislature staff; Judith Zafferini of the Hispanic-American Democrats, and Gov. Richard Riley of South Carolina, chairman of the subcommittee.

The committee also includes these Kennedy supporters; former senator Dick Clark, Sam Dawson of the United Steelworkers, former representative Patsy Mink, California Assemblyman Art Torres and Maxine Waters. Sen. Daniel Patrick Moynihan (D-N.Y.) is an "independent" member.