The veteran coach blamed a lack of concentration for his side's 2-0 defeat to Korea Republic, and is keen to get their SA2010 hopes back on track against Nigeria.
The two teams are due to meet in Bloemfontein on June 17 and Rehhagel says he will be expecting significant signs of improvement.
"Basically, we played into our opponents' hands from the seventh minute," he explained. "There were 18 people in the penalty area and if the ball is hit hard across it, anything can happen.
"The defenders failed to head it away and South Korea took full advantage. Having said that, you cannot always prevent those situations."
The 71-year-old German will then pit his side against Diego Maradona's Argentina, knowing that having points on the board will be essential by then.
"We have got to examine the last match very carefully and then we will try to improve in a very sober manner and learn our lessons," he said.
"But we are coming up against the strongest teams in the group now."