Hinkley said his team did not play the way he wanted them to play but did enough at critical moments to win the game.
"If you don't play at your best you get into a bit of dogfight and even at your best you're still going to have to fight really hard to get the result you want. But in the end we were able to be strong enough – and I think that is a good sign – we were able to be strong enough when it counted," Hinkley said.
He acknowledged that Melbourne was a much-improved side and had to take much of the credit for the tightness of the contest.
"We might just be a step or two in front of where Melbourne are coming from," Hinkley said.
"[We were] really strong in the last 10 minutes of the game, where we looked like we just had that little bit more experience to play the game the way we wanted to play."
The coach said the Power managed to tighten up its defensive efforts in the second half, restricting Melbourne to 43 entries inside the forward 50 after conceding 25 in the first half.
"I think in the end that won us the game," Hinkley said.
He said although Port Adelaide was on top of the ladder after losing just one game in the first 10 rounds, it was conscious of how much of the season remained.
Next week the Power comes up against St Kilda, coached by former director of coaching Alan Richardson, who remains a good friend of Hinkley.
"Richo will know a lot about us and we know a lot about what Richo's like. He'll be keen to do well," Hinkley said.
Port Adelaide plays St Kilda at the Adelaide Oval on Saturday afternoon.
