The 53-year-old admitted in the build-up to Saturday's match that he intended to "park the bus" in an attempt to stop the division's highest-scoring team finding a way through.
Sunderland kept their opponents at bay for more than three quarters of the game, but a Divock Origi strike and James Milner's penalty late on secured a 2-0 victory for Liverpool in front of their home supporters.
After the match, Jurgen Klopp claimed that Sunderland were "the most defensive team" he had ever seen, but Moyes has hit back at the criticism for the style of play utilised on Merseyside.
"We put [Jason Denayer] on [Philippe] Coutinho and man-marked him to try and nullify. My job was not to come here and entertain the Anfield crowd; my job was to come here and get a result for Sunderland," he is quoted as saying by The Sun.
"We had to try and do that. We didn't do that but tried hard to. Maybe if I was a foreign coach I would've been praised for that. We don't have the same quality as Liverpool. I knew we had to come here and defend. They won 6-1 here the other week so we didn't want to come here and get rolled over that easy.
"I was at the Euros all summer and saw a tournament like that. A tournament of big teams having to play against teams who shut up shop and made it difficult to get through. It's a big part of modern football now as well - it can't always be one-way. I hope soon I can come with a team that can give Liverpool an open game. At the moment I don't have the team to do that."
Sunderland dropped back to the bottom of the division as a result of the defeat, three points from safety ahead of next weekend's home clash with champions Leicester City.