The Wearside outfit reached the final of this competition last season before losing to Manchester City, knocking out Chelsea and Manchester United on the road to Wembley.
Poyet's side brushed aside Birmingham with a 3-0 success at St Andrews in the last round this term, but go into Tuesday's tie having yet to win in the Premier League following a goalless draw at Burnley on Saturday.
"It took us a while to get going and then we only managed to play the way I want for three or four minutes at a time, we weren't consistent enough," said the manager.
"We played okay, but okay is not enough, we need to play better than okay. We defended okay, we passed the ball okay, but we need to be better than that. If you just play okay, you are going to get punished."
Sunderland are unlikely to risk Emanuele Giaccherini after he limped off with a sore ankle at Turf Moor, while Steven Fletcher has a calf problem, but on-loan Inter midfielder Ricky Alvarez should be available after missing the weekend trip with a minor niggle.
For Stoke, Jon Walters sat out Saturday's 2-2 draw with QPR after suffering a knock in their loss to Leicester City a week earlier but he could be ready to return at the Stadium of Light.
Stephen Ireland is now fit again following a rib issue and deadline-day signing Oussama Assaidi is pushing for a first start back at the club.
Mark Hughes was left slightly frustrated after conceding a late equaliser in the weekend's stalemate at Loftus Road but Stoke remain unbeaten on the road this term following an earlier win at Manchester City and a draw at Hull City.
"The overriding feeling is that it was a missed opportunity - there are key areas of the game you need to navigate through and we didn't quite manage that," said Hughes. "We should have seen it out comfortably.
"But we've been good on the road this year, we're unbeaten on our travels and we've been to some difficult places, so that's the positive."
Hughes was also full of praise for Victor Moses after he put in another eye-catching display since joining on loan from Chelsea.
"He's been excellent in every game he's played for us," added Hughes. "He's given us that pace that we probably lacked last year and I think that's a marked difference in the way we are able to play away from home.
"He's going to get opportunities to play regularly for us and we've been delighted with what he's been able to produce."
