Mandzukic was left on the bench for Bayern's first two games after the winter break before returning to the starting lineup for Sunday's match against Eintracht Frankfurt, scoring a late goal to seal a 5-0 win for the champions.
"Mario Mandzukic is an extremely important player for us - but only if he plays to his full potential," Sammer is quoted as saying by the league's official website.
"He's been fantastic for us and is worth his weight in gold, but he must [perform well] consistently for us, even if it's not always easy. He's reacted well [to being left out], but he has to give more."
Mandzukic has scored 14 goals in 28 appearances in all competitions for Bayern so far this season.