"I'm trying to convince the players," Poyet told BBC Sport. "We have been working and talking, and it doesn't matter about our position, we just need to be ourselves, play the way that we play and keep going non-stop for 90 minutes.
"It's not easy, it's the most difficult part, you can play for long spells but to maintain the level and the belief for 90 minutes is very difficult. I think we are getting close to making that happen."
Despite their heroic advances into the semi-finals of the League Cup, however, a very harsh truth remains for the Black Cats when they re-enter Premier League action this weekend: they remain bottom of the table.
Sunderland are five points off safety and have accumulated just nine from their opening 16 games. They have also not won in their last five league games.
Yet, in the cup, the Black Cats cannot stop winning. The dispatching of the Blues means they do not have to fear anyone in the last four, while they have already beaten Manchester City this season.
Does their current form, however, mean that Poyet's side are going to do a Birmingham?
Under Alex McLeish, the midlands side won the Carling Cup in 2011 - beating Arsenal in a dramatic final - but suffered relegation from the top flight later in the season.
Sunderland fans will certainly hope for a different outcome but their contrasting form in the two competitions suggests it is a possibility, at the very least.
Birmingham were not the only side to win a cup and go down, either, with Wigan winning the FA Cup and getting relegated last season, too.
Bad omens are certainly there for the Black Cats, then, and Poyet will have to act fast if he does not want his side's cup triumphs to be soured by a poor league campaign.
image: © Ben Sutherland