The Saints boss made 10 changes to the side which drew 1-1 at Stoke on Saturday, while Gus Poyet retained only four of the men who lined up at Hull the same day.
He said: "We are a little bit disappointed to be out of the cup because it was an important competition for us to provide minutes for our squad and for our youngsters who, as you know, we like to use.
"We have a squad and we need to use all the players and give minutes in this type of game because the season is so long.
"In the next couple of months, we have a very tough period of games and we need everyone in the best form because sure, it will be important for the rest of the season.
"We are a little bit disappointed to lose important games like the game today, but this is football and we have to look forward.
"We have to say well done to Sunderland. They tried to win the game and they deserve, obviously, to be still in this competition."