I read how the 1968 Tet Offensive in Vietnam, though a major military defeat for North Vietnam, proved a shock to the American public who thought we were winning the war, and stirred up more domestic opposition against it.

Was there any similar incident that happened to the Soviet military when they were in Afghanistan?

No, the Soviet Union withdrew because they could no longer afford to fund the operation. By the late '80s, the USSR was beginning to implode due to the pressures of the West with the Cold War and the arms race. They could no longer afford to compete. Gorbachev saw the withdrawal and end to the conflict as a way to save money and preserve the Soviet Union. It was not totally successful since the USSR had totally collapsed and was dissolved by '93.

Also, the Soviet public was never told the truth and thought the Soviet Army was winning a great victory. They didn't have open/free media, so they believed whatever the state media apparatus was telling them. They even proclaimed the troops were returning because they had won and the war was over. The return of the conquering army type thing.