Victories over Olympiacos and West Ham, the former overturning a 2-0 UEFA Champions League last-16 deficit to secure United's progression, have served to dampen criticism of the Scot.
However, Moyes knows murmurings could intensify if seventh-placed United again come up short at home against a bitter rival following the recent 3-0 home loss to Liverpool.
While the Old Trafford faithful will be far from satisfied by another game in which their sole aim is to hinder a rival's Premier League title aspirations, a triumph would be a feather in the cap of the United boss.
"We'll go into our next game confident and ready to get a result," said a bullish Moyes after Saturday's 2-0 win at Upton Park.
Currently six points behind leaders Chelsea with three games in hand, Manuel Pellegrini's men head to their neighbours brimming with confidence after a 5-0 drubbing of Fulham at the weekend.
"I think that this team doesn't depend just on one striker," said Pellegrini. "Maybe in the last week we had some problems with Aguero and Jovetic.
"Now Jovetic is coming back and I hope Aguero will be next week with the team. If they don't score there are other players that will do it."
The pair, so often United's starting pair in recent years, seem certain to battle it out for a spot alongside Phil Jones at the heart of the defence.
Pellegrini's men were also 4-1 winners when the sides met back in September at the Etihad Stadium.
