The comments were made in a radio interview before the Phoenix's latest loss, a 7-1 thrashing by Sydney FC last Saturday, but only aired on Thursday.
The Wellington-based club sit at the bottom of the A-League ladder with four wins from 17 matches and have lost their past four games.
The Phoenix have featured in the last three A-League finals series, but are looking to embed a new, possession-based attacking style of football and have struggled for consistency.
Morgan said the Phoenix fanbase are in favour of a style change, but aren't willing to accept it will take time.
"People expect instant gratification, or they expect gain but no pain," he told RadioSport.
"It's just pathetic really. I can't think of any activity where you change like that and there's not a short-term cost as you go through the changes."
Morgan, currently in China, accused fans of not keeping the club's interests at heart.
"Fans are a cross-section of the public. A lot of them don't know much about the game and they certainly in my view think only of themselves and not of the future of the club.
"Some people, all they do is read the league tables and that's all there is to the game for them.
"They're pathetic really."
He said the club was making progress, but fans needed more patience.
"We're on the road - I think people have just got to be a little more sophisticated in their interpretation," he said.
Morgan is part of the Welnix Ltd consortium, headed by Kiwibank chairman Rob Morrison, which took over the Phoenix in September 2011 when founding owner Terry Serepisos stepped aside shortly before he was declared bankrupt.
Welnix also have a 12.5 per cent share as one of three private investors in the Hurricanes' Investment Ltd Partnership which will hold the Hurricanes' Super Rugby licence for the next three years.