Everton's winless run at home stretched to seven matches after a second-half goal from Benjamin Sesko settled a tight contest. The striker struck on the counter-attack as the hosts pushed forward in search of a breakthrough but were unable to find the decisive touch.
Despite the result, there was a positive reaction inside Hill Dickinson Stadium, with supporters staying behind to applaud the players at full-time â a marked contrast to the boos that followed the recent draw with Leeds United and defeat to AFC Bournemouth.
"I do, yeah, I thought they did well tonight," Moyes said when asked if he saw improvement. "I thought the crowd did great, I thought the players did great - they have done all season."
The Everton manager felt the game was decided by fine margins and insisted it could easily have gone the other way.
"I'm disappointed with the result. I'm happy enough with the second-half performance. I didn't think we did enough in the first half but overall we lost a really tight game that could have easily gone in our favour," he said.
Moyes also pointed to the difference in attacking quality, noting that Sesko arrived at Old Trafford in the summer for more than 70 million pounds - more than double the fee Everton paid for leading striker Thierno Barry.
"We narrowly beat United at Old Trafford 1-0 and probably shouldn't have won on the night but held out and got a result," Moyes added. "I thought they were a bit fortunate tonight. In the second half, we were probably the more likely team.
"But we couldn't get the goal. It's the quality - the quality which costs big money. We're just lacking that little bit where we could probably get a goal and we didn't quite."