Manager Steven Gerrard admitted he would speak to Tavernier about the situation after the right-back hit the post from 12 yards in last week's Europa League win over Feyenoord.
Tavernier had missed from the spot against Progres Niederkorn in the qualifiers in his only other attempt this season.
But the defender netted 14 times from 16 attempts last season and vowed to step up to the plate if Rangers get a penalty against Aberdeen on Saturday.
"I'll still be on penalties," Tavernier said.
"I believe in my ability and I've had some stick off a couple of the lads but I'm more than confident of stepping up and taking the next penalty.
"I took plenty of penalties last season. I missed maybe one or two last season, so I'm confident to come back and step up and deliver for the team."