The Demons' round three 94-point loss to West Coast came a week after a demoralising 148-point loss to Essendon and was the club's fifth-straight loss by more than 10 goals.
After winning just four games last season, Melbourne is on track for another horror year, currently sitting 17th on the ladder with just one win achieved against Greater Western Sydney.
The Power spent 2011 and 2012 languishing near the bottom of the ladder, but after making sweeping changes at player, coach and administrative levels, they remain undefeated in 2013.
In Adelaide to speak with both South Australian clubs, Demetriou said he hoped the Demons would follow the Port Adelaide example and recover lost respect.
"From an AFL perspective [what's happening at Port Adelaide] is what we love to see with all our clubs and that's what we hoping will happen with the Melbourne Football Club," Demetriou said.
"They're going through a difficult period at the moment, not unlike how clubs go through from time to time.
"I think Peter Jackson is starting there today and hopefully he can start to put things in place as well to help that football club."
The AFL's CEO said he was "absolutely thrilled" with the resurgence at Alberton.
He said the Port's recent success, on the back of two disappointing years in which it finished 16th and 14th, was reward for intelligent appointments throughout the club.
Coach Ken Hinkley, senior assistant Alan Richardson and celebrity chairman David Koch were all brought into the club last year and Demetriou said the Power had begun to see the benefits.
"If you get things right and if you get good people in place you can see a significant shift, you can see a significant improvement," he said.
"From the day David Koch was appointed as chairman, just the energy and enthusiasm that he's brought to the club, his desire to be successful, his desire to make sure he tries to nationalise the Port Adelaide brand has been remarkable.
"Then to appoint Ken Hinkley and of course Alan Richardson to the coaching panel and with a very fine CEO in place, they're putting together the basis of what forms a very good, strong football club."
Harry Thring is a reporter for AFL Media. Follow him on Twitter: @AFL_Harry
