Poyet's side, who suffered a 4-1 defeat to Arsenal in the Premier League on Saturday, take on Manchester City at Wembley next Sunday.
After seeing his charges beaten handsomely at the Emirates Stadium, compounding their relegation fears, Poyet hinted that several alterations could be made against City.
"Wembley could have been on the players' minds but this was a very good wake-up call," said the Uruguayan.
"No one has put them on the sheet for next week. Everything I had in mind for next week is gone in 90 minutes, gone completely, so we start from zero.
"Sometimes the players pick themselves. Now I have a few options. Maybe there are players pushing."
Sunderland will be looking to win the League Cup for the first time, having previously reached the final on one occasion in 1985.
They face a City side who have scored 19 goals and conceded just once in five games en route to the final.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.