The Democratic Party, in an extraordinary response to President Reagan's State of the Union speech last night, conceded a "resounding defeat" at his hands last November and portrayed itself as a "party that knows it has to change" to "earn anew the political respect of mainstream America."

Normally the out-of-power party responds to such presidential messages by taking the offensive and suggesting that state of the union is far shakier than the president described. But the Democrats last night appeared to be on the defensive, often turning their fire on themselves.

Almost ignoring Reagan except to acknowledge his political successes, the Democrats went on the air after Reagan's speech with a soul-searching, half-hour response that relied largely on Democrats who voted for the Republican president to plumb the depths of their own party's plight.

Almost like group therapy in its painful introspection, the program opened on a revealing note with observations from rank-and-file Democrats that Reagan's economic program appeared to be working and that Walter F. Mondale, his Democratic opponent in last fall's election, assured his own defeat by proposing to raise taxes.

"We said Reagan's program wouldn't work and to the extent that individuals are better off, it has worked, obviously at the price of the deficit," said a woman in one of the four post-election "focus groups" that were taped for the broadcast.

Said another: "One thing that pushed people over the edge, people that were borderline, was that Mondale came out and said, 'We're raising taxes.' And Reagan is saying, 'You're better off than you were four years ago.' Well, I think I'm better off; I'm definitely not worse off. I'm definitely going to be worse off if I get more taxes."

The program, aired on most but not all television networks, gave little more than cameo appearances to House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) and Senate Minority Leader Robert C. Byrd (D-W.Va.). It all but ignored most of the party's other current leaders, including its 1984 presidential contenders, and such other luminaries as Sen. Edward M. Kennedy (D-Mass.).

Instead, it gave honor-roll treatment to new-face figures described by narrator Bill Clinton, governor of Arkansas, as "bold leaders who are building bridges to the 21st Century," ranging from Gov. Mario M. Cuomo of New York to Mayor Tom Bradley of Los Angeles.

But the focus mainly was on 58 unnamed rank-and-file Democrats -- many of them under 40, "upwardly mobile," blue-collar as well as white-collar, supporters of Reagan -- who participated along with selected elected officials in the election post-mortem sessions.

The message seemed to be that the Democratic Party was listening and learning, benefiting from the lessons of its defeat, down but by no means out as it attempts to find its role for the future.

"As a political party which has suffered a serious defeat, we Democrats recognize that we must earn anew the political respect of mainstream Americans," said newly elected Democratic National Committee Chairman Paul G. Kirk Jr. in a statement issued in conjunction with the party broadcast.

"Our message today is that we are listening to America, assessing the state of the union with open minds, willing to move in new directions and determined to reclaim our rightful and legitimate heritage as the party that responds to the shared dreams of individual Americans."

Kirk called the "resounding reelection victory" of Reagan a "placement of trust by the American people."

The gentle treatment of Reagan was underscored by Clinton when he paused in the show to say, "By the way, Mr. President, happy birthday tonight."

In a somewhat more optimistic view, Rep. Tony Coelho (D-Calif.), chairman of the Democratic Congressional Campaign Committee, called Reagan "a very attractive Band Aid over a festering wound" and suggested that the Democrats' prospects look brighter when seen from below the presidential level and from the viewpoint of future leaders.

At a prebroadcast briefing on the Democratic response to Reagan's speech, Coelho noted that, while Reagan was carrying 49 of 50 states last fall, the Democrats were retaining control of the House, picking up seats in the Senate and nailing down three-fourths of the country's governorships. Reagan's victory, he said, was "a very personal one."

Striking a note somewhere in between, Clinton, as narrator of the program, conceded that the party suffered a "resounding defeat" and "knows it has to change." He added, "perhaps we have lagged behind in recent years but we're on the move now." In an attempt to define where the party is, Clinton said:

"America needs this revitalized Democratic Party because we will work for a government that will go beyond the prison of past thinking, a government that will work in partnership with the private sector to foster economic growth, a government that will operate its own programs with a commitment to excellence and accountability and independence from narrow interests, a government that will not turn away from problems that no people with a heart can ignore."

"Our critics have said we want too much government, while they want government off our backs. Well, we want the government off our backs, too, but we need it by our side."

Several Democrats, ranging from young rank-and-file voters to O'Neill, expressed frustration that many programs enacted over the years under Democratic pressure are now taken for granted, with the party getting no credit. Some of these are programs that Reagan now wants to cut, observed one of the participants.

The issue of budget deficits, which have grown threefold under Reagan and now hover around $200 billion, was one area in which the Democrats appeared to feel they had something going for them.

Social Security, an issue that has helped the party in congressional races, also seemed to get the adrenalin flowing.

In one of the groups, House Majority Leader James C. Wright Jr. (D-Tex.) responded to a question about Social Security by contending that Reagan appears to be backing off a campaign promise not to allow cuts in Social Security benefits. The Democratic-controlled House, said Wright, will "help him keep that promise."

But there also were conflicting messages in the broadcast that underscore the party's difficulties as it attempts to reconcile its loyalties with the pressures to bend them in the competition for younger voters. Within a minute or two of each other, a young man spoke favorably of the Great Society programs and then Virginia Gov. Charles S. Robb and Philadelphia Mayor W. Wilson Goode made a strong case for limited government.

From Byrd and O'Neill came expressions of concern over how to blend change and continuity. The Democratic Party is always willing to change but "people don't want the Democrats to lose their sense of fairness and compassion," Byrd said. Said O'Neill, in what appeared to be a reference to the contribution of Democratic-inspired programs over the years: "Yeah, I think they appreciate what we have out there, but they don't appreciate where we came from."