Mourinho was being taunted by a minority of Liverpool supporters when in the Chelsea dugout and responded by putting his finger on his lips when the Premiership leaders drew level through a Steven Gerrard own goal.
The Blues boss was sent off from the dugout but Allardyce says that the powers that be must focus on ejecting the abusive supporters and offer more protection to the coaches who are sat in the dugout.
"If you're being hurled abuse constantly then turn round and put you finger on your lips, how is that going to incite the crowd?Why don't the police and security get in there and rip a few of the abusive fans out and throw them out of the ground.
"The dugout areas are no longer protected enough against the fans. The abusers have started to create a lot of problems.We have got to have a serious look at the protection of players and staff in the dugout area." Allardyce said