The Reds currently sit five points and one position behind the sixth-placed Blues heading into this weekend's showdown.
Brazil midfielder Lucas knows a win for Liverpool at the weekend will be vital if they are to finish ahead of their neighbours and secure a top-six finish.
"We still have a chance of catching Everton and that's our target," said Lucas. "We know we have to win if we want to finish a position higher than we are now.
"Merseyside derbies are always special to play in. The atmosphere will be amazing at Anfield and it's the kind of game you really look forward to playing in.
"We will go into the derby with a lot of confidence. Hopefully we can get another win and try to finish the season on a bit of a high.
"It's been a difficult season for us but we have to keep going. We still have three games remaining and the chance to get nine more points. The manner of our victory against Newcastle showed the character of everyone."
Lucas says the 6-0 rout in the north-east shows how good the spirit in the Liverpool camp is at the moment and added: "We showed on Saturday that we are a team.
"We approached the game in the right way and played with a lot of confidence and intensity. After going 4-0 up in the second half, we just controlled the game. I remember when we beat Newcastle 5-1 at St James' Park a few years ago and this was even better.
"But even though we won 6-0 there are still areas that we can improve upon. We need to keep working and keep believing."