DENVER--A tearful Rep. Patricia Schroeder announced yesterday that she will not enter the race for the 1988 Democratic presidential nomination, saying, "I could not figure out how to run and not be separated from those I served."

Mrs. Schroeder, a veteran of 15 years in Congress, had spent nearly four months testing her potential political and financial support, and her announcement stunned supporters who gathered at noon in the outdoor Greek Theater in Denver's Civic Center Park.

"I learned a lot about America and I learned a lot about Pat Schroeder [this summer]. That's why I will not be a candidate for president. I could not figure out how to run," she said.

For a few moments, she was overcome with emotion and could not speak. Her husband, Jim, who stood beside her at the podium, urged her to "take a minute, take a minute" to compose herself before continuing her statement.

After wiping her face with a hand-kerchief, she continued, "I could not figure out how to run and not be separated from those I served. There must a way, but I haven't figured it out yet.

"I could not bear to turn every human contact into a photo opportunity."

Irene Natividad, chairwoman of National Women's Political Caucus, said Mrs. Schroeder had made "a smart, pragmatic political decision. I think it was the right thing to do."

"I think we're too mature as a movement to just go [into a campaign] for symbolic reasons," she added. "I'm grateful she went out there and kind of broke the door down as far as women being considered as serious presidential candidates.

"If not this year, a few years from now."

Sen. Paul Simon of Illinois, one of five announced Democratic candidates, called Mrs. Schroeder "a respected national leader whose views will help shape the course for America.

"Pat and I are very close on the key issues. I will welcome her counsel in the months ahead," Simon said.

Mrs. Schroeder, who coined the term "Teflon president" to refer to President Reagan and has referred to the announced Democratic contenders as "a bowl of unset Jello," urged her supporters to "build on gains we have made and not lose them.

"We must get America back to a government by the people, for the people."

She said there must be a way to marshal the grassroots support she tapped this summer "and find out some way to do it at the presidential level."

"I thank you, Denver. It's good to be back," she said.

Her organization reportedly had raised only half of the $2 million she once said was needed to run a credible campaign, despite a series of "Run, Pat, Run" fund-raisers held nationwide on September 20. Those gatherings had been expected to raise as much as $700,000, but her office never has released a figure on how much money actually was brought in.

Mrs. Schroeder, 47, also was thought to be reluctant to surrender her independence on the issues.

Two weeks ago, she said, "The minute I start talking to anybody professional in Washington, I start shuddering. They start talking about how you have to look presidential, how you've got to have at least 10 guys around you and they've got to be giving everybody body checks and throwing them out of the way."

Her decision leaves five announced candidates and one unannounced contender in the Democratic field. Rep. Richard Gephardt of Missouri, Sens. Simon of Illinois and Albert Gore of Tennessee, Massachusetts Gov. Michael Dukakis and former Arizona Gov. Bruce Babbitt have declared their candidacies, and civil rights activist Jesse Jackson plans to enter formally the race next month.