The Toffees suffered a 1-0 defeat to Sheffield United on Sunday, their ninth at Goodison Park this season.
"With this defeat, we've lost the opportunity to fight with more possibility of being in Europe next season," the Everton boss said.
"We lost a great opportunity; our chances are less now than before. We have two games left to play; we need to see which position we are in at the end.
"It's really difficult to explain what is going on here at home; we've lost a lot of games, all the same kind of games.
"I have to take the responsibility of this, I hope the players also take the responsibility. I am really embarrassed."