The Merseyside outfit - already certain to finish sixth in the table - will surpass their previous best haul of 65 by a point if they beat Chelsea in their season-closing fixture at Stamford Bridge tomorrow afternoon.
It is something Moyes, overseeing his last Everton match before departing to succeed the retiring Sir Alex Ferguson at Manchester United this summer, is keen to sign off with.
Three days after it was confirmed last week that he will be replacing Ferguson, the 50-year-old saw his side take all three points from his final Goodison Park game as Toffees boss when they defeated West Ham 2-0 on Sunday, a match at which the home supporters gave him a rapturous reception.
Reflecting on that encounter and looking ahead to the Chelsea contest, Moyes - who admits the last week or so has been "tough" for him emotionally - said: "We finished the West Ham game off very well last week.
"That has put us in a league position where we can't go any further up or any further down.
"That is great, but we want to try to get a record points total if we can - that would be our final goal.
"It is a good game to finish off with, and it is not a game where there is nothing there."
Chelsea - currently third and not yet guaranteed that spot, which ensures automatic qualification for the Champions League group stages - go into the fixture off the back of their triumph in Wednesday night's Europa League final.
Although sixth, Everton will not be involved in either continental competition next season, with European football only being earned via the league with a top-five finish this term after teams lower down the table in Swansea and Wigan qualified via their efforts in the domestic cups.
It is a reality that Moyes, given the campaign his side have had, admits has come as a considerable disappointment.
"In the year we qualified for the Champions League (2005, when they finished fourth to earn a place in the competition's qualifying rounds), the points we have (this season) would have been enough to get us there," Moyes said.
"But we don't even make Europa League football this year, which is really tough on us.
"It was something we really wanted to drive for, to get back to European football.
"I thought it was something we needed as a football club, so we are disappointed to miss out on that, and it was only maybe one or two weeks ago that we were beginning to think we probably wouldn't make the Champions League - we had always thought we had an outside chance."
Meanwhile, Moyes has confirmed that Everton captain Phil Neville has already played his final game for the club, with the 36-year-old defender not being fit enough to feature in tomorrow's contest.
Neville, who announced last month that his career as a Toffees player would not be extending beyond this season, misses out due to the knee problem that has been sidelining him recently, while a knee complaint will also prevent midfielder Leon Osman from being involved.