The Power's 20-point loss to Richmond at Etihad Stadium on Sunday capped a disappointing patch of four losses from five games.
Port now finds itself a game behind the top four sides – the Sydney Swans, Hawthorn, Geelong and Fremantle – having held top spot at round 14.
Richmond saw the Power as a significant scalp and Hinkley said it was clear his side could not cope with the heat.
"It comes with the territory and if you don't like that, well you'll give up your spot on the ladder," he said after the game.
Instead of shrinking away from the pressure, Hinkley wants his side to welcome the spotlight.
"For us, it's really damning and damaging for what we've been able to do so far this year that we've put ourselves in that position," he said.
"When people see that you've improved, people start to acknowledge that you've improved.
"Then when you start to show a few cracks they come after you."
Richmond outhustled the Power in a number of key areas - none more so than the contested possession count (125-159). "We were badly beaten inside (the contest) again. Contested possession was a significant disadvantage for us," Hinkley said.
"We're not playing OK at the moment; we've certainly got a lot of work to do to improve."
Turnovers from the back half also proved particularly costly, especially as the Tigers seized control of the match with a burst of seven goals in the second term.
Hinkley hopes his players can see the writing on the wall.
"Hopefully we've had our little down time in the season and the boys get a real sting in the tail," he said.
"I've seen a little bit of that, but I don't think they've really realised and been honest enough to say that there's some stuff not quite right with what they're doing.
"You've got to make sure you own your position. We haven't owned our position the last month"
If the players failed to recognise their faults, Hinkley said he would not be afraid to swing the changes as Port searched to get its season back on track.
A lengthy injury list compounds its problems, with ruckmen Jarrad Redden and Brent Renouf ruled out for the season and defenders Alipate Carlile (1-2 weeks) and Jackson Trengove (4-5 weeks) still a while away from making their returns.
"If you don't earn your spot in the side, you run the risk of losing your spot," Hinkley said.
"We give them a fair bit of trust – and you have to. You can't go chopping and changing because stability is really important.
"There comes a time where you have to say, nope that's not acceptable for Port Adelaide to play that way, and you have to let some people have that opportunity, if they deserve it, coming up from underneath."
Hinkley believes star forward Robbie Gray has escaped serious injury, despite having his head thumped into the Etihad Stadium turf late in the game.
He will be monitored this week ahead of Sunday's clash against Melbourne at Adelaide Oval.
