Hartlett lost his cool in the third quarter of the Power's 18-point loss to the Blues, striking Carlton captain Marc Murphy twice to the body before landing a forearm to his jaw.
After making a brilliant start to the season, Hartlett has been targeted by run-with opponents and he was again below his best on Sunday, battling close attention at times from Dennis Armfield and finishing with 15 possessions.
"You get a bit of pressure put on you and then you've got to keep your composure," Hinkley said of his team post-match.
"I certainly haven't seen the 'Hammer' (Hartlett) thing so I'm not too sure how bad [it is] or what it does or doesn't look like.
"Certainly you have a little bit of frustration, but that's something you've got to deal with.
"We certainly need our best players or our leaders to stand up at the right time."
Port Adelaide has lost three straight games, with Sunday's loss soured by a hamstring injury for Dom Cassisi, who is expected to miss three to four weeks.
Hinkley said the Power were "in the middle of a challenging little patch" but insisted his team was not fading after a 5-0 start to the season.
"We haven't handled the pressure [the opposition] have been able to put on us," he said.
"You see that with young teams; they have to handle that and they have to handle travelling and playing and coming up against good opponents and dealing with it.
"It's experience.
"Keep playing in those games and making better decisions as you go through those games and you turn those into wins."
Port fell 34 points down in the third quarter but kicked five goals to three in the last term to limit the final margin.
Hinkley said he was pleased with his players' ability to "hang tough" but he was disappointed with their lack of composure.
"Carlton left us in the game a little bit at times when they missed some shots," he said.
"Our composure, I reckon, showed up a little bit and our ability to handle a bit of pressure from a mature side.
"We didn't handle that the way we need to, but that's a learning curve for us.
"In the last couple of weeks, we've almost looked like we're ready to get going and then we'll make a poor skill error."
Hinkley said substitute Kane Mitchell, who has worn the green vest in five of his six games, would be considered for a full game next week after sparking the Power in the fourth quarter.
"We've played him in a full game against the Kangaroos and he wasn't quite as effective for us," Hinkley said.
"It's a tactical move for us to say he's probably going to be able to add something into the game at the right time.
"Whether he gets the chance to start, that's something we'll go through thoroughly through the week and hopefully for Kane's sake he gets to start.
"We think he certainly adds to us."
Nathan Schmook is a reporter for AFL Media. Follow him on Twitter: @AFL_Nathan
