Moyes, who replaced Sir Alex Ferguson during the summer, has witnessed four home defeats in 11 Premier League games this season which has left the club seventh in the table.
During his time in Manchester, Ferguson won 13 league titles and two Champions Leagues, along with many other trophies, but Queiroz has confidence in Moyes turning things around.
The Portuguese coach is currently in charge of the Iran national team, having also spent a number of seasons as Ferguson's assistant manager.
And regarding Moyes, Queiroz said: "That is the present situation, the fans, David and the players are not happy.
"I know how much the players have a strong wish and determination to come back and I'm sure in a short period of time they will find the right track and it is just a matter of time.
"It is my strong belief, because I know the club and it is very strong, when the board make a decision they trust the people they chose.
"And I'm sure with the qualities and experience David has, plus the wonderful work he did at Everton and the support of the entire board, soon the results will come out and everything will be all right."
Queiroz also dismissed suggestions that Ferguson should stop attending United games amid claims his presence is not helping Moyes.
He added: "What do you expect? That Sir Alex Ferguson doesn't watch the games? That is pure, pure fantasy.
"Do you expect that Sir Bobby Charlton doesn't see Manchester United or Carlos Queiroz doesn't see Manchester United? We love the club, we should be there all the time.
"I hope that, given good health, he will be there for years and years to see the club he has been building for his entire life - the club he loves.
"I'm sure all the coaches, the manager and players love to see him in the stands."