Moyes believes United weren't as bad as their Goodison Park scoreline suggests.
First-half goals from Leighton Baines and Kevin Mirallas consigned Moyes' side to an 11th defeat of the season on his first return to Goodison Park since taking over at Old Trafford.
The result has condemned United to their lowest points tally in the Premier League era with Champions League qualification now mathematically impossible for the reigning champions.
But Moyes claims that there were positives in his side's performance during the opening 45 minutes against the Toffees.
"We played very well in the first half and to go in two-nil down wasn't what I expected," he told his post-match press conference.
"We had passed the ball really well but didn't have the final pass, the killer through ball or the little bit that was needed in the final third.
"It was disappointing but I didn't think we deserved to go in two-nil down at half-time, that was for sure.
"We had good play and control of the game. We had a bulk of the ball and they were a threat, Everton, on the break. The [first] goal was a big kick up the pitch from Ross Barkley, nodded down and picked up.
"For us to concede a goal like that was terrible. The second one was a better move but we should have defended it much better than we did.
"I thought we had good periods of possession but we didn't have the through pass or enough to create enough chances in the first-half."