A goalless draw in the 220th Merseyside derby damaged their bid to catch fifth-placed Tottenham, who are now five points ahead, and extended their win-less run at Anfield to 14 years.
Everton may be just a point behind the 61 they had when they qualified for the Champions League in 2005 but football has moved on and that haul no longer guarantees entry into the Europa League.
They need two points from their remaining two matches to record their best total and also ensure a second successive finish above Liverpool - for the first time in the top flight since 1937.
"It is not something which has happened that often - finishing above Liverpool," said Moyes.
"It is not something we look out for and I am sure it is not something Liverpool look out for.
"It shows we are trying to make progress against a lot of the other good sides in the division.
"But the only thing that does matter is the European picture for us at Everton.
"We are trying to get back among the bigger boys and play on that stage as regularly as we possibly can.
"We have already nearly got the best total we've ever had. We had 61 when we qualified (for the Champions League) and we've got 60 now so we've had a pretty good season.
"It will be disappointing if we don't get rewarded for it but we'll try to win the last two games and see if we can get rewarded.
"The comfort for me would be to qualify for Europe. That would be my main objective, it doesn't change."
Moyes felt his he would have finally ended his winless streak at Anfield - Everton have not enjoyed a victory there since 1999 - had a key decision gone their way.
Sylvain Distin's second-half header was disallowed by referee Michael Oliver for a push on goalkeeper Jose Reina by Victor Anichebe.
Moyes disagreed, saying: "It was a legitimate goal.
"The referee said Victor impeded the goalkeeper but the goalkeeper ran into him so it can't possibly be a free-kick.
"It is not a foul. It is disappointing because it is not easy here.
"You people (the media) are quick to remind me I've not won at Anfield but if you don't get any decisions at Anfield it makes it very difficult to win and that (not getting decisions) is quite a regular occurrence when you come here.
"If you score a good goal you need to get something going for you."