The Wearside outfit were dumped out of the FA Cup at the quarter-final stage by Hull City last weekend just a week after losing the League Cup final against Manchester City.
Sunderland now turn their attention to a crunch Premier League clash with fellow strugglers Crystal Palace on Saturday and head coach Poyet has warned his players that there are no distractions now as they strive to avoid the drop.
The former Brighton and Hove Albion manager said: "It's a relief to have that sorted in certain ways.
"I was a fan when I was young and I went to the stadium and wanted to see my favourite player on the pitch and I would blame the manager when he didn't play him. We all do that.
"We are all managers and we are all fans. You don't realise at that time what is going on behind the scenes.
"How long it took for someone to sort out the tickets for the final for example, you would not believe. You give players and staff a certain amount of tickets but sooner or later you know they are going to come and ask for more and then somebody else does and you never finish.
"How can you control that and sort everything else out as well? It's impossible.
"Even on the day before. Now there is nothing, no distractions. There is no Wembley, no tickets, no summer, no pre-season. It's only me they know is preparing things and we have to concentrate on winning football games.
"That is perfection. That's what we all want and I think that's one of the best things about being in England.
"They don't have to talk to the press every two days like in other countries. They have nothing to worry about apart from sleeping well, eating well, training well and be ready to give their maximum.
"It's impossible to ask them to win every game, but just to give their maximum. Everything is in place for them to do that."
Poyet will have a fully fit squad to select from when Tony Pulis' side travel to the Stadium of Light.
