The Merseyside outfit were unable to recover in their quarter-final against Wigan Athletic after they were hit with three goals in four minutes last weekend.
Following their exit, the Toffees have been preparing to take on English champions Manchester City in the Premier League as they try to clinch a spot in Europe by the end of the season.
"It's not only the fact that we're out of the cup it's the way we went out," the Liverpool Daily Post quotes Distin as saying.
"It's hard to take. It's also a bit like last season. This time we've gone out at the quarter final point and have to play City. We have to carry on."
Everton are currently seven points adrift of a Champions League place in the table.