Already eliminated from the Europa League, Unsworth named a much-changed XI at Goodison Park, where the Toffees found themselves still in the game at 2-1 down with four minutes of normal time remaining.
But a porous defence - which has now conceded 16 goals in six matches under Unsworth - was breached three times in the closing stages, leaving the interim manager far from pleased after giving some members of his squad the chance to impress ahead of Sunday's trip to Southampton.
"I'd like to think every single player is hurting the way I am at the moment and if they are not then they shouldn't be here at this great club," said Unsworth.
"The minimum requirement is 100 per cent effort. Only those players will know themselves when they look themselves in the mirror at night.
"The players who have been asking me for opportunities to play in the first team were given that.
"I asked the players to make it difficult for me to leave them out of the team on Sunday and the majority have probably made it very easy for me.
"The manner we capitulated [in] just isn't acceptable and the players know that.
"What you can't do at this level is carry players. When your best player is an 18-year-old kid [Beni Baningime] who's only had a couple of first-team appearances that tells you all you need to know.
"Players need to take responsibility - senior players, foreign players, young players. Everton fans will be disappointed with what they saw and so am I."