"As a proud Everton man I am hurting and I think I have to tell the Everton fans how much it hurts me as much as it hurts them," he said on Tuesday.
"Sometimes players will take the easy way out and shirk responsibility. I'm asking players to perform. I think when you're in a tough moment, in this day and age, the mentality of players isn't what it used to be.
"I just want the players to be ready for a fight. I will stand side-to-side with them if they give me that attitude. Those players who have not got the bottle to stand up for the fight need to be honest and say it.
"In January we might need to recruit proven Premier League players who are up for the fight."
Unsworth said that talks were progressing over appointing a new manager but nothing has been finalised. British media have reported that former England manager Sam Allardyce is favourite for the job, with Shakhtar Donetsk coach Paulo Fonseca an alternative. Unsworth has also put his name forward.
"Sam's a top manager but it would be wrong of me to talk about names," he said. "Whoever gets the honour will have my full support and backing."
Asked if Wednesday's game at Goodison Park would be his last as caretaker, Unsworth replied: "I don't know, is the honest answer. If not we'll come in on Thursday and keep rolling." He added that he would have no problem going back to his previous role as Under 23s manager.
Unsworth also said that defenders Leighton Baines and Michael Keane were both doubtful for the "must-win game" against West Ham, who are managed by former Everton boss David Moyes.
The Merseyside club are 16th in the league standings, two points and places ahead of the Hammers.
(Reporting by Neil Robinson; Editing by Christian Radnedge)
