Everton blew a 2-0 lead to allow United to earn the draw with two late goals.
Moyes said afterwards: "I think it should have been more. When we were 2-0 up, we had chances to make it 3-0. We were up against a good side, I know they are not in a good place in the table. We did as well as we could do."
On the injury-time penalty call being overruled by VAR, Moyes said: "I thought Ashley Young's jersey is undoubtedly pulled. I thought the on-field decision was correct and I was surprised that the referee was sent to VAR. It went against us today, we won't complain too much about it. That decision went against us."
He continued: "Today's result was a good result, we lost two points and gave away two poor goals but we played well in front of the crowd and overall I'm really pleased.
"Suddenly now people are looking at Everton a bit. More points, new stadium, hopefully, that will be in the Premier League."
On Idrissa Gueye's performance, Moyes added: "He's been doing great, he's played really, really well and he is keeping it going. He does a great job for the team."