Liverpool manager Roy Hodgson admits his side are in a "predicament" after they slipped to second bottom in the Barclays Premier League following defeat in the Merseyside derby.
However, the 63-year-old refused to accept that the situation was worsening and believes his players are showing signs of improvement.
Tim Cahill, in the 34th minute, and Mikel Arteta, in the 49th, scored the goals which ended a run of three successive league derby defeats for the Toffees.
Liverpool have won just once in the Premier League and gone six matches in all competitions without a victory.
"We are not trying to disguise the fact this is a predicament, or any other word you care to use," said Hodgson.
"For any team to take six points from eight games at the start of a season is a predicament but maybe you could argue being Liverpool the predicament is greater."
He added: "We didn't win the game and therefore people will read a lot of things into the performance."