United sit seventh in the Premier League with 12 games remaining of Moyes' first season in charge since he took over following the retirement of Alex Ferguson.
The defending Premier League champions are 15 points behind leaders Chelsea and 11 adrift of Liverpool, who occupy the final UEFA Champions League qualification place.
Moyes has been heavily criticised for United's disappointing form this term, but Queiroz - a former assistant to Ferguson - has urged United to keep the faith with the ex-Everton boss.
"The success of Manchester United was based on a couple of principles," the Iran coach said in quotes reported by the Daily Mirror.
"The first thing was it had a good foundation of consistency, continuity, trust and confidence.
"The other thing I learned when I was at the club: the club always had a strong belief with the people that work inside it - they trust themselves.
"I want to believe that it is just a tough time at the moment and in a short period of time we will see the Manchester United everyone expects.
"I have been in that experience and the most important feeling is to trust each other, believe each other, and make the right decisions. If you are not able to win today, I am sure tomorrow things will be right. I think they need to be given time."
Queiroz worked as Ferguson's deputy in the 2002-03 season before returning for a four-year stint following a brief spell in charge of Real Madrid.
The former Portugal boss feels it was inevitable that Moyes would struggle in his first year, but has backed the 50-year-old to turn things around.
"I knew changing coach would not be easy," Queiroz added. "To cross this bridge after Sir Alex being with the team for so many years, in one way, I think we were always going to have to expect some difficult moments. It is natural.
"But I am very much confident. The club has a lot of experience; it is strong; it has a persistent culture. I am sure David Moyes in a short period in time will do the right things at the club and the team will start to perform."
