The Black Cats hadn't won at Anfield since 1983, a run of 19 games in all competitions, and set up to frustrate the hosts - who had scored 17 goals in just five previous Premier League games on home soil.
And they did well to thwart Liverpool until their stubborn resistance was finally broken on 75 minutes, Divock Origi's cross-cum-shot surprising Jordan Pickford to find the bottom corner.
Didier Ndong's trip on Sadio Mane then gifted James Milner the opportunity to seal the win for Jürgen Klopp's men, sending Pickford the wrong way from 12 yards.
It denied Sunderland the chance to record three consecutive league wins, and back-to-back away games, for the first time since April and May 2014 as their wait for a win over Liverpool - home or away - also stretched to nine games.
We've still got a long way to go, admits Moyes
Moyes told his post-match press conference: "I thought we got to the point where it was taking the manager to get the crowd going. We’d frustrated them for long periods."
The Scot said that it was "always going to be a difficult job coming here and playing them" as he hailed Liverpool's "great attack" which he said is "great going forward" in "everything they do."
"They're probably the best attacking team in the Premier League at this present time," continued Moyes. "We had to make sure we did our job defensively and then try and create opportunities when we could."
He spoke of the "great chance" that he felt his team fashioned at 0-0 for Duncan Watmore, but referred to the "small margins" within the game due to the fact they didn't score from it.
"We sometimes need to take it and we didn't do so," the Sunderland boss said, mentioning that his side are "having to come on a long way" and yet have still "got a long way to go."
Moyes insisted that after being "pleased with two great results recently" then Anfield is "the last place you'd want to come", reiterating that it was "always going to be difficult" for his team.
Regardless of the size of the task, Moyes felt that his players "did a great job in managing the game" as he accepted that they "knew this way the way we'd go" but praised them for still trying "to create chances few and far between."
He revealed that their pre-match tactics were to avoid playing with "the ball too much at the back" which would have allowed "Liverpool to press and do all those things that they want to do."
Moyes also said that the North East outfit "were going to try and make sure that Philippe Coutinho couldn't dictate and dominate the game that way he's in many games this season" and that they "had to try and do as good a job [as possible]."
"In the end it wasn't good enough," he admitted. "But I think the difference in quality of the two squads will probably give you the reasons for that as well."
Sunderland boss: We should have done better with 'great' Watmore chance
Liverpool saw a number of chances come and go and just before Origi's late opener, it appeared Sunderland's resilient game plan was going to pay dividends for them.
But mid-way through the second, Klopp turned to the crowd and encouraged them to up the ante - with the frustrations of the home support seeping down to the players as poor first touches and wayward passes continually let them down.
Moyes added: "The crowd are certainly with the manager here, which is great for them. He’s able to influence the crowd and did so. We had started to frustrate them for periods."
He admitted that Liverpool had "missed chances as well" and so it wasn't all Sunderland's work that turned up the tensions on L4 and also once again brought up the "great chance" he felt his team had.
He added that when Victor Anichebe found Watmore in space inside the box, the latter could "either shoot first time with his left or quickly control it and get a shot away" and further bemoaned that the winger failed to do either.
"They were the small, small things. We needed one of them to go for us if we could," explained Moyes. "I thought we defended well and stuck to the task. You know what it's like when the crowd get going here. We tried to keep them quiet for as long a time as we could."
Moyes did at least take heart from the manner in which his team thwarted Liverpool, restricting them to very few clear opportunities and particularly limiting them to little in a largely dour first-half.
On how well his side defended, he declared that he doesn't know of any "good teams" that aren't "first and foremost defensively sound" and said teams need to have "a right good defence" and "good organisation" whether they are fighting for the title or trying to avoid relegation.
He also acknowledged that Sunderland have "not been good enough recently" in that respect and added: "Today we did a job, but it still wasn't good enough. But I have to praise the players. Against the opposition and the quality of players we were playing against, I think you'd say that the players stuck to the task and came pretty close."