The Anfield side suffered their third successive home loss in the 3-2 defeat by Udinese in the Europa Cup on Thursday night.
Rodgers’ managerial stock rose at Swansea as a result of the way in which he got the Welsh side playing attractive passing football.
But legendary former Liverpool goalkeeper Grobbelaar feels those tactics can be costly when used in defensive situations.
“Does he [Rodgers] tell the defenders not to tackle in the box?” Grobbelaar told talkSPORT.
“The ball came into the Liverpool box [against Udinese] and they allowed the opposition striker to juggle the ball in front of [Jamie] Carragher. The other central defender could have kicked the ball away three times but he allowed the ball to be passed to [Giovanni] Pasquale."
Liverpool completed three times as many passes as their Serie A opponents but Grobbelaar believes the defenders need to focus on the basics and clear the danger without being overly concerned with retaining possession.
“If you get the chance [as a defender] to lump the ball out of the box, do it,” added the 54-year-old.