Defending champions United returned to winning ways with a 2-0 home victory over Swansea City on Saturday after three straight 2-1 defeats in league and cup action.
The victory over the side they lost at home to in the FA Cup last week came after Moyes made a tactical move at halftime, with Shinji Kagawa and Adnan Januzaj switching roles which resulted in a 47th minute goal for Antonio Valencia.
"He felt we could get down the left and made a subtle change by moving Adnan out there and Shinji in behind the striker," Fletcher told Manchester United TV of his manager's ploy.
"He also told us to raise the tempo, press a little bit quicker in their half and not let them get into their rhythm of passing the ball because they are one of the best passing teams in the league.
"We knew the right back was on a yellow card so that (moving Januzaj to left wing) was an opportunity to get at him because he couldn't give away too many fouls or else he would run the risk of getting a red card."
Former boss Ferguson was not in the crowd to see the victory at Old Trafford sealed when Danny Welbeck scored in the 59th minute but he did watch the loss to Swansea and Capital One Cup semi-final first leg defeat at Sunderland from the stands.
Ferguson has been a keen spectator at United games this season since retiring after 27 years at the helm in May but fellow Scot Fletcher dismissed media suggestions that the former manager's attendance at matches was putting on unfair pressure.
"It gets us angry because we know it is not true," he said.
Moyes was equally dismissive of the suggestion.
"It tells you that people don't know me, they don't know Sir Alex. People are only saying it because they have no idea about how it works," Moyes told the club's channel.
"Sir Alex has been fantastic, incredibly supportive, he's only there to help me. I have a conversation with him when I need it. I tend to see him for a minute or two after the games, we'll have a chat and I've found him great."
Ferguson might travel to London to watch United take on title chasing Chelsea on Sunday with similar doubts about strike duo Wayne Rooney and Robin Van Persie making the trip.
"A chance," Moyes said of Rooney's chances of recovering from an abductor injury in time to play.
"Less of a chance," was the view of Van Persie's struggles with a thigh injury.
A fifth win in six league games should provide some relief from the relentless criticism and evaluation of the former Everton manager's fledgling Old Trafford tenure but an away success at Chelsea would really help sway the detractors.
Brazilian fullback Rafael da Silva, whose twin brother Fabio was sent off minutes after coming on against Sunderland, said the criticism of Moyes was misplaced.
"We are the ones who have to take the responsibility," he was quoted as saying by British media after the Swansea win.
"We have to show, like we did in the second half. I don't know why everyone is looking at the manager. It is the players who have to do the job on the pitch.
"We are together. We knew there would be a change. The manager had just left after 27 years. It was always going to be hard. We have to take the mentality David Moyes has given us and use it on the pitch."