The Toffees could have leapfrogged the Reds into seventh in the Premier League had they recorded their first win at Anfield in Moyes' 10-year reign - however, a Steven Gerrard hat-trick won the match, and the Scot revealed his disappointment with how each goal came from an Everton mistake.
“We had the opportunity to play a key pass and we didn’t, they scored from that,” Moyes told reporters.
"We gave the second one away on the halfway line and the third one from the halfway line as well. We were at fault for the goals.
“The first 20 minutes, Liverpool gave us a real going-over, which we expected. We did well to weather it and we knew it was going to happen.
“I actually thought when Liverpool scored that we were probably the better team at that time, so that was the disappointing thing. We went in 1-0 down and we hadn’t done all that badly.
“I thought we were on the front foot at the start of the second half, and we gave it away and they went on to score.
“Liverpool had chances, they could have scored more. We missed some chances but they did as well.”
Despite the heavy defeat, Everton still sit in ninth position in the Premier League having lost just one of their last 10 games.
And Moyes claims that he is happy with a return of three points from their previous two fixtures.
He continued: “Had you said to me before the Spurs game ‘you will get two draws’ I would have said ‘that’s okay’, as it is, I have got three points from the two games.”