Last season's Premier League champions beak Olympiakos 3-0 to qualify for the Champions League quarter-finals on Wednesday but the result did not represent United's overall fortunes this season.
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"I think the big thing was I could look at the supporters in the face after the game on Wednesday night because I thought we had given them something to shout about, we had nothing to be ashamed of with our performance," the 50-year-old told reporters on Friday.
"In some other games I have felt ashamed because the team haven't played well enough and I've not got a team out which has got a good result."
Moyes also confirmed that Robin van Persie will miss this weekend's trip to West Ham - but that the club have not received anything conclusive on the Dutchman's injury, one he picked up against Olympiakos after scoring a hat-trick.
"We're getting Robin re-scanned today (Friday)," he said. "We're not quite conclusive on everything we've seen.
"We want to just check that out and be sure. He won't be available for tomorrow's game, but we'll try to give you some update when we can on the outcome of it."
United travel to a West Ham outfit who have won the past three home matches and Moyes is well aware of the threat posed by Sam Allardyce's men.
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"I don't know if that was his curse last week or if it's still to come this week. But he's done great. They were at a lower league position and he's turned them around.
"We've got a lot of games coming up, we need to make sure that the squad's ready for all the games. That's big for us, that we have all our players fit and available."