Diogo Jota struck in the second-half for Liverpool's 1-0 win, though Everton insist Luis Diaz was interfering in play from an offside position in the lead up.
“There are lots of things I'm happy with,” Moyes told evertontv. “The two games we've had against a team who at the moment are leading the Premier League (have been close). And right up to the end, we were still in with a shout of getting something out of the game.
“Their goal is offside, there's no doubt about that. It's a mistake by the linesman or VAR or the referee, whoever you want to say. It's quite easy to read as well, it's not even a difficult one, if you ask me. But not surprised that decision at Anfield you don't get.
“We had one or two good opportunities. Probably the bit where we were getting ready to make the opportunity to make the chance to score, we didn't complete the final pass and we didn't really make it as well as we should have done.
“But, look, I have to say, I think the players have done an awful lot of good stuff tonight. They've tried to stick up against a side who are a top side at the moment. Liverpool played much better tonight, much more aggressive, tougher than the first game. Maybe we're just beginning to get a bit closer to them generally, and I think that over the two games the results have shown we're not as far away maybe as we think we are.”
Moyes added: “We're off the back of nine undefeated so the players had no reason not to believe we would have a chance.
“We just never got control of the game. When we did get the chance to play we didn't play particularly well with the ball or not as well as we need. But, we're just trying to get better. If you'd given me this position, as we've said many times, eight weeks ago or so, I'd have snapped your hand off for it. I actually think we've had to play Liverpool twice in a month or so now and I think we've given them pretty good games.”