Lucas Leiva claims UEFA Champions League football is still achievable, although the midfielder insists Liverpool are cautiously optimistic on their chances of a top-four finish.
Saturday's 1-1 home draw with Wigan Athletic tempered Reds' hopes of returning to Europe's elite as Steve Gohouri's equaliser after Raul Meireles' opener left the Merseysiders trailing fourth-placed Tottenham Hotspur by eight points, having also played a game more.
Liverpool had won four games on the trot before the Anfield setback and Lucas believes Kenny Dalglish's side have shown enough in the last month that they can close the gap on Spurs.
But the 24-year-old, who made his 100th Premier League appearance against the Latics, is realistic on the Reds' chances.
"I don't think it would be clever on our part as a team to talk about the top four because two months ago we were three points off the relegation zone," said the Brazil international.
"It is clear the team has improved and we are playing better but we have to keep going.
"In football everything can happen but we can take each game at a time.
"We should have killed the game and got three points but we move on and we have two important games in the Europa League now (against Sparta Prague).
"There are still a lot of things to improve but our record is not too bad even with a draw.
"We know we must keep the same level of concentration every game to make sure we finish as high as possible in the table."
The quick turnaround in fortunes has been achieved since the arrival of Dalglish, who took over from Roy Hodgson just over a month ago, and former Chelsea assistant manager Steve Clarke, who was recruited as first-team coach.
Dalglish has taken 14 points from seven Premier League matches to transform Liverpool's season after Hodgson had taken them dangerously close to the bottom of the table.
All the squad have spoken highly about the influence the Liverpool legend has had on every part of their daily working life.
Lucas had been having a good season anyway but his performances have gone up a level since the change in manager.
"We know how good he was as a player and we can see he has a lot of knowledge about football and also Steve Clarke is helping the team a lot," said the 24-year-old.
"It is the little advice Kenny gives to us, he knows a lot about football and the way we have to play and the way Liverpool played in previous seasons so we want to do what he asks us.
"Every day there is little advice and you have to listen and take it on the pitch.
"When you believe in a manager it is really important and when he gives you advice you have to listen. He says things to make us think about things."
Lucas' achievement in reaching 100 Premier League appearances has surprised even the player himself, who was derided by many fans for his first three seasons after arriving from Gremio in the summer of 2007.
"I don't think too many Brazilians have achieved this mark in the Premier League but hopefully there are many games to come and I'm looking forward to playing them," he added.
"I didn't think I would get 20 Premier League appearances to be honest but I am still here and improving all the time.
"I am pleased the way I am playing. I think everyone can see how I have changed.
"In my first season I was only young and a boy learning about English football.
"It is a great achievement but nothing changes, as a player I always try to work hard and be positive.
"I am not the kind of player who likes to talk too much, I prefer to work a lot and try to do it on the pitch.
"I am really settled and feeling comfortable on the pitch. Hopefully I will keep working and keep improving."