"We are feeling the pressure ... we have just got a little spooked," Hinkley said.
"We're not as brave as we want to be. But that is something that can come back.
"We started the journey about trying to get a little bit of respect - we got a bit of respect back. But when you get some respect back, you get a bit more attention.
"The next part for us is to be able to handle that."
The Power's win was just their second in five games, coinciding with a slide from top spot to fifth.
Their nail-biting triumph was largely created by the midfield exploits of Robbie Gray (26 disposals, eight clearances) and Ollie Wines (26 touches, seven clearances), and the influence of utility Justin Westhoff (21 possessions, two goals).
And while Hinkley acknowledged a batch of his players were struggling to find form, he praised the tenacity of Melbourne, who appeared headed for a heavy loss when five goals down midway through the second quarter.
"We were hurting ourselves with ball movement and stuff at times but…we got back on track with tackling and contested possession," he said.
The Power will now enjoy their bye as part of the split round and could see the return of several key players for their next game against Collingwood.
With the exception of any setbacks, key defender Alipate Carlile (hamstring) will be available, as will Angus Monfries (hamstring).
Hinkley said there was a slim possibility Jackson Trengove (ankle) could also play, although it was more likely he would return against the Sydney Swans in round 20.
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