Everton lost their Europa League tie 5-1 at Goodison Park.
Unsworth insists the uncertainty over the manager's position is no excuse for the players.
"I hope not, I really hope not," he said.
“And I would love to think that every single player is hurting the way I am at the moment. If they are not hurting the way I am at the moment then they shouldn't be here at this great club, they need to know what this great club is all about and that the minimum requirement is 100% effort, commitment and desire and there's your building block to perform and play good football.
“My answer is: I hope not. But only those players will know themselves when they look themselves in the mirror at night."
He went onto add: “Tonight is a shock and the manner of the defeat and the last 10 minutes was totally unacceptable."
Unsworth continued, “We're asking players to run harder, to work harder and get the ball a bit quicker than they are used to and some can and some can't.
“What you can't do at this level of football is carry players and when you're best player is an 18-year-old kid who's only had a couple of performances in the first-team, that tells you everything you need to know.
“Tonight was a little bit different but players have to take a responsibility - that's senior players, that's foreign players, that's young players – whoever puts on that shirt has a responsibility to give their all and the Everton fans will be disappointed with what they saw tonight, and so am I."