The 35-year-old feels that a repeat of their first-leg performance at the back on Tuesday would see them exit the Champions League at the hands of Carlo Ancelotti's men
The Bundesliga champions suffered a 1-0 loss in Madrid in the first leg of the Champions League semi-final and host the Spanish giants on Tuesday for the return leg.
Bayern prepared for the decider with a 5-2 win over Werder Bremen but their defensive problems were highlighted as they twice had to come from behind in the game. Both of the goals that Pep Guardiola's men conceded were on the break and Pizarro says that the same mistakes would be just as costly against Los Blancos.
"We conceded two goals via counterattacks in the first half. We can't afford to let that happen against Real, so we'll have to be on our toes," the Peruvian told the press.
"We played well in the second half and managed to score the goals to win the game. It was important that we won the match today and I hope we can do the same on Tuesday."
Bayern attacker Thomas Muller preferred to look ahead, with his team concentrated on the Champions League having sealed the Bundesliga title in March.
"I don't want to go into great detail about our win today. It's all about Tuesday's match for us and we need all the support we can get from everyone at the club," he remarked.