Fowler, 34, who is in the middle of a two-year contract, watched from the stands, heightening speculation that he may be finished at the club.
But Fury chairman Don Matheson said both Fowler and Ferguson had agreed to stay committed for the duration of their contracts following talks on Monday.
"I?ve spoken to them today and realise there has been a misunderstanding," Matheson said in a statement.
"Ian wanted to play a particular formation and that included utilising Robbie as an impact player off the bench and Robbie believed he wasn?t part of the squad.
"There has been an unfortunate outcome because of that misunderstanding."
Matheson said the issue had been sorted out between the pair and they had given a commitment to try and win Fury's three remaining matches of the season.
"The club apologises to the fans for what?s happened, but moving forward I am happy that we?ve been able to resolve this in the best interests of the club and the game," he said.
Matheson said Fowler was frustrated by speculation that he would be quitting.
"Robbie is getting pretty tired of the speculation that he will be leaving North Queensland Fury FC. He is not leaving the club," said Matheseon.
"He and his family have made some sacrifices for him to play for North Queensland and he?s happy with his decision."
Fowler told a British newspaper last week that his wife was finding it tough to adjust in Townsville, where Fury are based.
The former Liverpool star is the highest-profile signing in the five years of the A-League.
He is playing club football outside England for the first time since he finished as the fourth-highest all-time scorer with 161 goals in the Premier League.
Fowler's manager, George Scott, later played down the events of the weekend.
"There was a bit of a misunderstanding and that's all it was," Scott said.
"He's alright, he's fine there. He's under contract, so at the moment he's a Fury player so he'll
Source: AFP European Edition