City dominated possession but lacked incisiveness around goal at AAMI Park until Pollicina entered the game at halftime, created multiple chances and then won a penalty for Emina Ekic to score in the 60th minute.
"She's one of the best players in this league," Vidosic said.
"She's showing it now every week and last week was excellent - (player) of the match, scored two.
"We want to look after her. Normally you don't want to (substitute) someone that's (player) of the match and hitting form and take them off.
"We always want, as a substitute, that impact and she was great."
The victory was soured by an ankle injury to Ekic that forced her substitution 10 minutes after the goal.
Ekic was weaving through the attacking 18-yard box and attempted to cut inside, lost the ball then after lunging to retrieve it, got her left ankle awkwardly caught underneath her.
The 23-year-old received treatment on the pitch before walking off with assistance.
"She's a little bit hobbled at the moment," Vidosic said.
"She said it's painful. It's on her ankle.
"We're not sure from the bench what happened - everyone heard a bit of a scream.
"We'll see probably in the next day or two the extent of the injury. We hope it's nothing too serious and hopefully we don't lose her for too long."
City dominated possession in the first half but struggled to create genuine goalscoring opportunities, with Perth having the best chance of the first half in the 40th minute.
Centre-back Naomi Chinnama came to Melissa Barbieri's rescue, making a huge goal-saving block on Cyera Hintzen after the Glory forward had danced around the veteran goalkeeper.
City found a new sense of urgency when Pollicina entered the game at halftime and got their chance from the penalty spot in the 60th minute.
Pollicina attempted to break through Perth's defensive lines and defender Kim Carroll bundled the attacker into teammate Isabella Wallhead.
Ekic buried a low, hard penalty into the bottom corner.
Hintzen blasted over the bar in the 85th minute as Perth pressed for an equaliser but failed to find a way through.
"The team put everything out there," Perth coach Alex Epakis said.
"There were moments where I believe we had more clear-cut chances then they may have had, other than the penalty.
"We could have got something out of it."
