The Black Cats booked their place in the FA Cup fourth round with a 3-1 home victory over League One Carlisle on Sunday afternoon, but immediately turned their thoughts to Tuesday night's Capital One Cup semi-final first leg clash with Manchester United.
However, Poyet insists his players will relish another tough game more than the training they would otherwise be doing.
He said: "When I was a player, I wanted to play. I hated to train and the fitness coach making me run and run. I wanted to play games.
"If it was three days [between games], it would be perfection; if it's two days it's a little bit risky.
"Today we gave a rest to a few players who will be fresh on Tuesday and will have no excuses to perform against Manchester United."
Sunderland eventually eased past Graham Kavanagh's men after weathering a first-half fightback at the Stadium of Light.
They looked to be on their way to victory when England international Adam Johnson curled a fine 33rd-minute free-kick past keeper Greg Fleming.
However, the visitors were back in it within nine minutes when keeper Vito Mannone failed to cut out David Amoo's cross and Matty Robson thumped the loose ball home off the underside of the bar.
But the respite was short-lived and when skipper Sean O'Hanlon unwittingly turned Johnson's driven 50th-minute cross into his own goal, the writing was on the ball with substitute El-Hadji Ba making sure that the death.
Poyet was especially pleased with the performance of Ki Sung-yueng, who was forced to abandon his usual midfield role to line up at centre-half with Valentin Roberge and Modibo Diakite having joined John O'Shea on the sidelines.
But he was equally delighted with the contributions from youngsters Ba and Duncan Watmore, who provided exciting second-half cameos.
Poyet said: "I like them. I wouldn't like to kill them, I would like them to slowly become part of this football club.
"There are always opportunities for one reason or another, because of the opposition or when we play or because of the momentum or because you play in two days' time or because we have got injuries or suspensions.
"They need to be ready and then do what they did today, Duncan and Ba, to jump in and then show the manager and show everybody that they are very, very interesting players with a great future."
Despite the result, Kavanagh was a proud man as he headed away from his former club.
He said: "I am very proud, very, very proud. I am disappointed, obviously, with the result, but the way we played, the intelligence we showed - I thought tactically, we were excellent.
"We looked to counter-attack in the game and in the first half, I thought we created the better chances, but we just couldn't get over the line with the victory.
"But I am extremely proud today."