A grim-faced President Reagan vowed yesterday to continue the confirmation battle for Supreme Court nominee Robert H. Bork, but some administration strategists acknowledged privately that the fight seems lost.

"I don't think that it's decided yet, and I'm working my head off to make sure we don't lose it," Reagan told reporters outside the Oval Office after a day in which he had received steady doses of bad news about Bork's confirmation chances.

One administration source said, "White House officials are more pessimistic than the president. They think now that it's going to be very hard for Judge Bork, because the southern Democrats don't seem to be coming over."

Making no attempt to conceal his disappointment at the increasing number of senators who have declared opposition to Bork, Reagan said, "Frankly, I think it has become a disgraceful situation because I think the process of confirming a Supreme Court nominee has been reduced to a political, partisan struggle."

One official familiar with the president's thinking said Reagan is not convinced that Bork's nomination should be withdrawn. He said the president would not decide on his next step until he meets today with senators listed as undecided by the White House.

William L. Ball III, chief White House legislative liaison, told reporters that his count showed 42 senators against Bork, 40 for him and 18 undecided.

Privately, however, administration officials conceded that, even by that count, the White House would have great difficulty winning enough of the undecideds to gain confirmation.

"It is certainly uphill, and the slope has gotten steeper today," a White House official said. "But it's still climbable, and the president has put on his mountain gear."

Until yesterday, administration officials maintained that Reagan had no "backup strategy" for Bork and would insist on an up-or-down vote. They said any suggestion that a replacement was even being discussed would be seen as admission of defeat.

Now, some of these officials say political realism requires that Reagan be prepared for defeat or withdrawal. In that case, they say, he should be ready to submit a new nominee almost immediately.

"Some of the Republican senators see that and some members of the White House staff see that, but Reagan isn't there yet," one administration source said.

Bork met for 20 minutes with Reagan yesterday and longer with other White House officials. Sources said the question of withdrawal was not discussed, and Reagan said in his appearance with reporters that he "hadn't even thought" of compiling alternative names.

The name most frequently mentioned as a prospective nominee if Bork withdraws is Patrick E. Higginbotham, 48, an Alabama native and graduate of the University of Alabama Law School. He was named by President Gerald R. Ford as a federal trial judge in Dallas in 1976 and promoted to the 5th U.S. Circuit Court of Appeals by Reagan in 1982.

Sources said Higginbotham, described in the Almanac of the American Judiciary as "moderately conservative," was on the administration's short list when Bork was chosen.

He is considered more liberal than Bork on such issues as abortion rights, access to courts and constitutional interpretation and is believed more likely to attract southern Democratic votes eluding the administration in the Bork fight.

As momentum built against Bork in Congress, Reagan met with about a dozen major corporate executives supporting the nomination and asked them to call undecided senators to press for Bork.

"Bork deserved to be confirmed. That was his message," David Roderick, chairman and chief executive officer of USX, said of the president.

Staff writers Ruth Marcus and Dale Russakoff contributed to this report.