Tapp was forced off the ground after injuring his left knee in the opening half of the Mariners' stalemate at Industree Group Stadium on Saturday.
After shaking off an earlier knock in wet conditions, the 23-year-old midfielder went to ground after changing direction in a contest just in front of goal.
Tapp had suffered an anterior cruciate ligament injury in 2022 and missed the Mariners' 2022/23 championship campaign.
Central Coast are already without skipper Trent Sainsbury (chest) and winger Miguel Di Pizio (knee).
Sainsbury is not expected back until the new year, while Di Pizio's return is unclear after the teenager underwent surgery.
Adding more salt to the wound, the reigning champions are now winless with three consecutive draws.
"It was a dominant performance from us. We just lacked the goals and the end product," Mariners coach Mark Jackson said.
"To get three points, you have to put the ball in the back of the net and we didn't do that."
Perth (0-2) also continue their search for victory under new coach David Zdrilic.
"It was a very nervy start but the very good thing for us was that we were able to get back into the game and take the sting out of the game," he said.
"Coming here is not easy ... Another day, it could've gone either way but we're happy with the point."
The hosts thought they were given the chance to break the deadlock when the referee pointed to the spot, but the penalty was overturned after video review.
Mikael Doka, searching for Ryan Edmondson, sent the ball across the face of goal in the 76th minute before hitting Perth defender Luis Canga's arm.
But it was adjudged to have struck Canga's arm in a natural position, much to the chagrin of the Mariners and their faithful.
Luis Canga points to where he thinks the ball hit him after the referee penalised him for handball. (Steven Markham/AAP PHOTOS)
Central Coast academy product Sasha Kuzevski almost broke through for a goal in the third minute, but was denied in a moment of shared defensive brilliance by Perth's Jarrod Carluccio and goalkeeper Oli Sail.
Carluccio first deflected Kuzevski's shot with a header, before Sail palmed off the threat.
A poor pass from Mariners keeper Dylan Peraic-Cullen almost opened the door for the visitors in the 19th minute, but Brandon O'Neill was off target.
Kuzevski continued to pepper the goal and sent the ball across the face in the 53rd minute for the Mariners' best shot at scoring.
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