Ronald Reagan carried his campaign againt President Carter into the South today, accusing his opponent of abandoning both his home region and the presidential debate.

"Jimmy Carter has turned his back on the problems you face in the South," Reagan told an applauding crowd of several thousand in a downtown Knoxville square. ". . . Well, don't feel lonely about that. Your problems are not all he's turned his back on. When I challenged him to the kind of debate the majority of the American people want, he turned his back on me."

Reagan was in high spirits as he opened a week of long distance campaigning which will take him into four southern states easily carried by Carter in 1976 and then into four western states that were swept by Gerald R. Ford.

The Republican nominee told aides he thought he was a winner in his nationallly televised debate Sunday night in Baltimore with independent candidate John B. Anderson.

The Reagan strategy in the wake of the Baltimore event, as it was before, is to depict Carter as "a jogger . . . running away from his record," a man afraid to debate.

"You know that there was one fella missing," Reagan quipped. "It was his night to go out and tear Teddy Kennedy bumper stickers off. Seriously, he was home watching a movie, "Third Man Out.'"

Despite the quips and the jibes, there no longer seems to be serious expectation in the Reagan camp that the GOP nominee and Carter will ever debate. Nor is it likely that Reagan will face Anderson again.

Leaving his hotel this morning in Baltimore, Reagan said "saw no need" for another debate with Anderson and would leave the question of debating Carter to his negotiators.

Later Republican national chairman Bill Brock said he doubted if there would be more debates.

"We've probably seen the last debate," Brock said. "It seems to be in Carter's interests to avoid it, and it's hard to see how either side can get out of the standards they've established."

Brock, a former Tennessee senator, and Senate Minority Leader Howard H. Baker Jr. (Tenn.) said that Carter has a lead in Tennessee of 5 percentage points or less but is vulnerable.

Reagan's southern strategy for 1980 is to concentrate on what some of his aides call "the outer South." The prime targets, after the big-state battlegrounds of Texas and Florida, are Virginia, Mississippi, Louisiana and Tennessee.

The cutting edge in Tennessee, according to Brock and Baker, is an economy where the unemployment rate is over 10 percent in 48 counties.

Reagan hit hard on economic themes today, coming up with a "family suffering index" he said has increased more than threefold during the Carter administration.

But the Republican nominee also was careful to praise the Tennessee Valley Authority, which he used to cite as a prime example of federal government bureaucracy and inefficiency.

Reagan's appearance here was dogged, as it has been in other places, by pickets waving signs and chanting "ERA, ERA." Reagan usually ignores the Equal Rights Amendment supporters, but today he interrupted his speech and told them that as president he would work to see that legislation against sexual bias was enforced and that new laws would be passed if needed.

"I know there's a great serious distance between our people about this, but I believe we're all united on equal rights for all and equal rights for women," Reagan said.

"I happen to disagree with the amendment for the simple reason that I believe the amendment will take out of the hands of elected representatives the problems of discrimination and put them in the hands of the courts, and who knows what judicial decisions will be made there. It will take about 20 years or so before enough decisions are made to alter what discriminations there might be."