The nation's long, bitter coal strike ended officially yesterday just as it began 110 days ago with most Americans hardly noticing the difference.

Despite claims of an imminent national emergency when it invoked the Taft-Hartley Act in a futile attempt to end the strike 16 days ago, the Carter administration - in one big collective sigh of relief - declared that the nation had survived quite well indeed.

"This nation has endured a long strike without widespread unemployment or drastic reductions in electric power," said President Carter in a statement hailing the United Mine Workers' vote Friday to ratify a new three-year contract, which was to be signed formally at the UMW headquarters here last night.

This represented a considerably rosier picture than the administration presented March 9 in warning of job layoffs totalling 3.5 million by mid-April, impending threats to the nation's defense and foreign policies and other dire consequences. At the time, Carter also said contract negotiations had reached an impasse, leaving a Taft-Hartley back-to-work order as the only viable option.

But that was before the stalemated talks resumed and produced a contract, which Carter described yesterday as a vindication of the "important principle of industrywide bargaining between the coal operators and the UMW."

Joining forces for a strike post-mortem in the White House press briefing room, Energy Secretary James R. Schlesinger and Labor Secretary Ray Marshall denied that the administration had been "crying wolf." The situation simply looked worse then than it does now, they said.

The "day of reckoning" was postponed, said Schlesinger, when the nation rallied around the hard-hit East-Central region, cooperating to boost the area's weekly coal deliveries from 300,000 tons in early February to 1.5 million tons by last week.

The nation "once again demonstrated (its) capacity to respond to difficult circumstances," he added, and gave itself additional time for the collective bargaining process to work its will.

The euphoria over the long-sought settlement was dimmed, however, by both immediate and long-range problems affecting peace and producitivity in the coalfields.

Despite a final tally showing that the contract was ratified by a vote of 58,384 to 44,210, or 57 percent, the UMW's planned return to the mines on Monday may be hampered by pickets representing construction workers and retired miners.

Negotiations to complete a contract for 14,000 UMW construction workers were under way yesterday, and Marshall said an agreement was expected by Monday or shortly thereafter. Three years ago, construction workers picketed and closed down many mines for several weeks until they got a contract of their own. And this year, a number of UMW pensioners have threatened to picket the mines to protest the main UMW contract's failure to raise their pensions to the level offered new retirees.

But Marshall said yesterday he expected a "substantial number" of the 160,000 striking miners to be on the job Monday, with the work force gradually rising back to normal as the week progresses.

More important were the long-range problems that government, industry and union officials agreed were not solved by the new contract, which included a 39 percent wage-and-benefit increase by 1980 but did not contain earlier industry demands for stiff wildcat strike curbs and other "labor-stabilizing" measures.

To "address the industry's long-range problems," Carter reiterated yesterday his intention to appoint a presidential commission on the coal industry to help resolve the industry's deep-rooted problems of health, safety and productivity.

"Friday's agreement, coupled with the work of this commission, will enable the coal industry to take its rightful place as one of the foundations of our long-term energy strategy," said Carter.

Marshall and Schlesinger agreed it may not be a simple task.

Both the UMW and the Bituminous Coal Operators Association, the industry's bargaining group, recognize that wildcat strikes and other production disruptions only strengthen the rapidly growing non-UMW sector of the industry, which now accounts for about half the nation's coal production, said Marshall. But "some fairly deeply entrenched hostilities" remain that were not helped any by the recent strike, he added.

The new contract guarantees payment of health and pension benefits and provides for some improvement in grievance procedures in an attempt to remove the cause of much recent wildcat striking, but few coalfield observers believe this will solve the problem.

"As gratifying as the vote was, it doesn't show overwhelming endorsement of the contract," said Marshall.

Schlesinger said the administration's hope for a massive energy shift from foreign oil to domestic coal hinges on solving these "institutional problems in the coalfields." The shift may be delayed, he said, "but it is inevitable."

Marshall also defended the administration against a crossfire of charges that it intervened both prematurely and belatedly. By prodding the parties to reach an earlier agreement that was overwhelmingly rejected by the strikers three weeks ago, he said, it set the stage for the eventual settlement. "This particular settlement would have been much more difficult if we hadn't intervened," he said.

Speaking for the coal industry, which was not universally pleased with the administration's performance, BCOA President Joseph P. Brennan expressed appreciation for Carter for "permitting the collective bargaining process to conclude these negotiations" - an apparent reference to the final round of talks that were conducted without governmental intervention.

Brennan also noted that industrywide bargaining had survived "its most severe test" since it was launched in 1950. Marshall also took note of this, describing a threatened breakup of industrywide negotiations, which the administration was quietly encouraging in the form of localized settlements, as the catalyst that forged the final agreement.