The needed taste of victory within the White House over tentative settlement of the coal strike must be tempered by the role played by Robert Strauss, the indispensable insider enlisted at the 11th hour for his long experience in how power really works.

Strauss, the notable establishment politician in an administration of outsiders, not only contacted executives of steel companies that own coal mines but also was the central figure pressuring other coal operators to accept the union's last offer. The reality for President Carter was this: Nobody else had the experience or contacts for that mission. But Strauss, splitting his time between being chief trade negotiator and cabinet member without portfolio, is spread too thin.

His role belies the claim of administration officials (especially Strauss himself) that the Carter team was well prepared for the coal strike. The truth is closer to this candid appraisal by one middle-level official closely connected to the coal crisis: "Our grade was 'D,' a step ahead of failure. It was good only when compared with the Marston affair, because this one almost got away from us."

That "D" seems a trifle harsh, considering that the president met his desperate need to show success somewhere. The belated exercise of presidential power was essential to sagging self-confidence at the White House. Still, the unstructured, impromptu approach to handling the crisis spells danger ahead.

Contrary to natural White House efforts to rewrite history, the coal question was wholly in the hands of Labor Secretary Ray Marshall until mid-February. Marshall, a college professor without labor-mediation experience, had devised no thorough strategy. Coal-state politicians and administration officials privately concede Marshall was given an assignment beyond his capabilities.

One reason is the idiosyncratic arrangement of the White House staff. Top aide Hamilton Jordan handles a vast array of political questions from coal to Panama. In addition, both labor relations and the canal treaties are under the same Jordan assistant, Landon Butler. While devoting every waking hour to the treaties, they could not focus on coal. When Jordan and Butler belatedly turned full attention to coal after the union's bargaining council rejected a negotiated settlement Feb. 12, their effectiveness was limited by lack of experience. And neither had the contacts needed to pressure coal owners into a settlement, which quickly became the necessary administration strategy.

Enter Strauss on Feb. 19. Ironically, a president elected partly for being separated from the establishment has repeatedly turned to Strauss, a quintessential establishment figure. By Feb. 22, Strauss was making telephone calls that he alone among Carter's men was capable of making.

Strauss, a millionaire Dallas lawyer, placed a call to Dallas to the president of First International Bancshares, Dewey Presley, who has a corporate connection to Continental Oil Company, owner of Consolidated Coal Company. Would Presley tell Continental Board Chairman Howard Blauvelt to expect a call from Bob Strauss? Strauss then called Blauvelt, with the message he was giving all coal operators: "You can't fine-tune this negotiation." In other words, the last United Mine Workers offer is the best you'll get.

Strauss's telephone found Edgar Speer, chairman of U.S. Stell (an important coal mine owner) undergoing a routine physical checkup at the Mayo Clinic. Strauss asked Speer's help in winning industry acceptance of the UMW offer. When Speer agreed, Strauss turned on his ingratiating drawl of insult and self-depreciation: Relying on you, Speer, is like relying on Joe Namath to play quarterback with two gimpy knees.

Although that style is inimitable, the harsh fact is that nobody at the White House is really comfortable even telephoning big, gruff Ed Speer at his office, much less at the Mayo Clinic. Thus, one West Virginia Democrat, an expert in coal politics, believes the late-starting Carter effort was grounded in fear of failure, then recovered in "superb" style - but primarily, he adds, because of Strauss.

Strauss is seriously overworked in his two-hatted job. So the ending of the coal crisis adds credence to recommendations by worried Carter aides that the White House staff must be reorganized and buttressed with experienced men of the world - even from the hated establishment.

Senior presidential staffers may be correct in calling the coal crisis one of a kind, not likely to be repeated. But handling that crisis "a step ahead of failure" - assuming UMW approval of the contract - should be a warning that the White House is not yet equipped to cope with the unknown.