The Merseyside derby was the last played at Goodison Park before Everton's move to their new stadium.
The match was a typical thriller, with James Tarkowski hitting an injury-time equaliser. Abdoulaye Doucoure, Liverpool midfielder Curtis Jones and manager Arne Slot were all sent off at fulltime.
Moyes said afterwards: "It was an incredible volley (for Tarkowski's goal). He didn't have the best game last week so he's made up for it with a goal in the last minute. It was a great goal but then it was a wait for VAR, we weren't sure if we were going to get the decision or not. I think it seemed to be a really tight call but fortunately it went out way.
"We made a good start and I thought in the second half we played well, looked more likely than Liverpool to score. When they scored I thought 'oh, well this is just going to be one of those days'. We're just a little bit short of when the moment comes in the final third to have the quality to finish at times. It started to look as if it was difficult but we got an incredibly good goal at the end. It was a great point which keeps our position in the Premier League a little stronger."
On being four games unbeaten, he added: "If you'd have given that to me before I came in I'd have taken it all day. We've got a long way to go, there's so much we can do to improve greatly and try to get back to the levels I believe we can get back to. Hopefully the light's shining on us if we can get through this season and the new owners come in and help us build a new team and a new better level of performances from Everton."