The 18th-placed side held off the Premier League title contenders for 40 minutes, before Steven Gerrard broke the deadlock and Daniel Sturridge added to their tally shortly after the break.
Sunderland remained in contention throughout, though, and a period of possession led to them causing a nervy end for Liverpool as Ki Sung-Yueng headed home Adam Johnson's corner.
The Black Cats had the opportunity to level the scores just before full time when John O'Shea met a Johnson free kick, but the defender could not steer his header on target.
Despite ending 2-1 losers, Poyet believes Sunderland defied their critics, who predicted an emphatic Liverpool victory.
"I think we can take a lot from that," he told Sky Sports.
"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."
After falling at the final hurdle in the the Capital One Cup, Sunderland returned to a relegation dogfight and Poyet fails to see why they cannot perform as well against fellow strugglers as they did against Wednesday's opponents.
"It's killing me," the Uruguayan coach joked.
"How it is possible that you can play away and finish with that kind of quality but not against teams at the bottom, I don't understand.
"We need goals, that is the key. We need to feel alright after tonight because not many people were expecting that."
Ki's goal brought an air of tension to Merseyside and Poyet admits seeing the home fans silenced was a compliment to his side.
"The feeling of seeing this crowd quiet at the end and then really excited when they celebrate at the end shows it was not an easy day for Liverpool," he claimed.
Poyet opted to deploy a flat-back five-man defence, with two holding midfielders, in a bid to hold out Liverpool but the introduction of Ki and Johnson offered attacking fervour.
"I think we were always in shape and making it difficult but we were not individually very good on the ball.
"Of course, Ki and Adam Johnson, if they have one quality is being outstanding on the ball and we take that risk to get back in the game.
"They made a difference and now in the dressing room the boys are thanking them because we needed them in the game."
Liverpool's first goal came courtesy of a free kick on the edge of the box after Santiago Vergini dragged down Luis Suarez on the edge of the box and Poyet admits his player may have been lucky to only receive a yellow card.
"I think it is very difficult," he added.
"If you see it from the moment the foul is committed, probably he is the last man.
"I didn't see it on television but sometimes it can be a red as well, I think the referee had a decent game."