A difficult week for the Scot ended on a high note on Saturday as his team beat Aston Villa 4-1 at Old Trafford.
An airborne protest against Moyes backfired as the home support rallied around their beleaguered manager during a comfortable win which came courtesy of a brace from Wayne Rooney, plus goals from Juan Mata and Javier Hernandez.
The win, which moved United to within 10 points of the Barclays Premier League top four, was a welcome boost to morale after the 3-0 defeat to Manchester City in midweek, but Moyes knows a tougher task awaits his team when Bayern Munich come to Old Trafford on Tuesday night.
Pep Guardiola's stellar team won the Bundesliga last week with seven games to spare, but Moyes sees the Champions League quarter-final as an opportunity to ease some of the pain that has been caused by a disappointing campaign.
"It's been a difficult season for us but we can go a long way to doing an awful lot better if we can get a result on Tuesday," the United boss said.
"The players are incredibly focused and I am really looking forward to the game."
If the fans who clubbed together the £840 for the 'Wrong One - Moyes Out' banner thought the stunt would trigger open dissent towards Moyes, then they guessed wrong.
The home fans inside Old Trafford booed when the plane appeared and Moyes' name was sung on a few occasions, particularly in the second half when it became apparent that United were going to win by a considerable margin.
"The majority of people are very supportive," Moyes said.
"They understand the job we are doing. We know we have a big job to do here and we are determined to put it right."
Moyes' biggest signing since he took over at Old Trafford, Juan Mata, put on his best display in a United shirt on Saturday.
Robin van Persie's injury means Mata has been shifted from the right into the number 10 position where he excelled at Chelsea.
Mata won successive player of the year awards at the London club because of his exploits in that position and from his exploits against Villa, it is easy to see why.
The Spaniard linked well with Rooney, Ashley Young and Shinji Kagawa as part of a dynamic front four, and he got the goal he deserved in the second half by prodding home Marouane Fellaini's pass to make it 3-1.
The 25-year-old scored 32 goals in his final two seasons at Chelsea and now he hopes to notch many more for his current employers.
"It felt very good to score," Mata told MUTV.
"It's taken a few games but I felt that it was coming.
"I feel very happy and very grateful to the fans who were supporting me.
"I will try to score as many as I can between now and the end of the season,and hopefully it is the first of many in my Manchester United career."
On another day all the post-match praise would have gone to Ashley Westwood for the way he curled the ball over the wall and past David de Gea to put Villa ahead after 11 minutes, but the midfielder was left to ponder what might have been after the final whistle.
"It was very special to score at Old Trafford, but to lose the game it takes the feeling off it a bit," Westwood told AVTV.
Villa could have taken something from the game had Christian Benteke not missed three good chances, but Westwood was loathe to criticise the striker.
"We are not going to get on at Christian for that," Westwood added.
"He scored enough goals last year and this year. People make mistakes in football. I am sure he will bounce back."