Jurgen Klopp’s side won a sixth European Cup in June, less than a month after they were pipped by Manchester City to the league title by a single point.
The league resumes on Saturday with Liverpool eight points clear of City and favourites to win their first top-flight title for 30 years.
“I think that is what our fans want,” Moore told the Press Association. “We were so close last year, 97 points, and in any other year we would have won it.
“But the club goes on and I think that (a league title), for many of our fans, would sit alongside our Champions League triumph as the barometer of success.”
City have been the domestic benchmark for their rivals, with four Premier League titles, four League Cups and two FA Cups since 2011, but Moore said Liverpool were following their own path.
“What Liverpool had to do was bring in a world-class manager, which we have, bring in a world-class squad, which we have, play exciting football, bring in players that are going to draw crowds no matter where they go, we’ve done that, build financial security at the club, we’ve done that.”
Moore said the Champions League victory had had a huge impact on the club, lifting them back to the level of “European royalty”.
Nine years ago Fenway Sports Group, then New England Sports Ventures, completed their £300 million ($380 million) purchase of the club.
They inherited a club languishing towards the foot of the Premier League with six points from their opening seven matches during the short-lived reign of Roy Hodgson.
“When we look at the health of the club, our revenues have doubled in the last five years and been reinvested back into the squad,” said Moore. “We have steadied the ship from some dark days nine years ago.
“We take great pride in our business model: a self-sustaining football club.
“He (Klopp) has built the chemistry and these players are content, motivated and excited to win — not just for Jurgen and the coaching staff but for the people of Liverpool and broader global fanbase.”
