The Black Cats boss believes that his players silenced their critics, who were predicting an emphatic win for the Merseysiders, by matching the Reds for lengthy spells.
"I think we can take a lot from that," Poyet told Sky Sports News.
"In the press everything was set here for a four, five, six, seven nil, a party, they would run all over Sunderland, which we didn't like.
"For the first time we played a different system and I think for a long, long period we really frustrated Liverpool."
The result leaves Sunderland in 18th place in the table, three points from safety with a game in hand on Crystal Palace above them.