But Doughty told BBC Radio Nottingham: "We have a fantastic manager here, and one of the reasons he is fantastic is that he is demanding of everybody.
"You wouldn't want to back a manager who was accepting of his lot."
Last week, Davies suggested that reports of a bust-up with the board were wide of the mark.
"I have not complained, had a grievance or a discussion with any of the board or transfer acquisition committee," Davies said.
"There are many things written about the manager - he's been disciplined, he's resigning or he's fallen out with the board. It doesn't exist."
Doughty added: "I think you have to take it with a little bit of a pinch of salt at times and there is a game to be played."
Despite finishing third in the table last season, Forest are yet to make a new signing this summer.
"It would be easy for me to bring in a number of people who would not improve our squad," said Doughty.
"We have one or two targets of top-class Championship level and one or two targets of up-and-coming stars from the Premiership stable."
Forest made nine signings last summer, but also failed to add to their squad in January - much to Davies' frustration.
But Doughty believes that is partly down to Davies' desire to be the best and insists Forest are backing their boss.
Can Forest challenge for promotion again this season? "I've been very privileged in my career to work with a lot of talented people. When you work with talented people, they always want more," explained the Forest chairman.
"Billy and I giggle, 'Do we need 90 more players to get promoted Billy? Four more strikers?' We giggle about it ourselves and we respect each other.
"We're backing Billy and the reason we are investing is because we've got probably the best manager in the game at this level and in my view someone who'll go on to much greater things.
"He's very talented, I think he deserves our support and we'll try to give it to him."