Ten points separate Liverpool and fourth-placed Arsenal and with just 10 matches of the season left it appears a return to Europe's elite club competition will be out of their grasp.
But Gerrard will not concede defeat until the Barclays Premier League table tells him otherwise but he knows they have to put together a consistent run of wins to stand a chance.
"It is a mountain to climb but at Liverpool you never give up," said the 31-year-old.
"We need to just win as many games as we can and see where it takes us but we won't give up until it is impossible."
Gerrard's hat-trick - on his 400th league appearance - in the 3-0 victory in Tuesday night's 217th Merseyside derby ended a run of three consecutive league defeats.
While two of those were at Manchester United and at home to Arsenal the other was at Sunderland, where Kenny Dalglish's side fell well below the standard required.
Liverpool's best performances, although not necessarily results, have come against the established top sides and in big matches but Gerrard admits they cannot just turn it on when the occasion calls for it.
"I suppose at times against the teams outside the top four maybe we have been more inconsistent and we have done really well against the top sides," he added.
"But to do well in this league you have to beat the sides that are down there as well.
"The league is getting stronger and stronger each year. To finish in the top four you have to be consistent, you can't choose when you turn up.
"You can't be eight out of 10 one week and two or three out of 10 the next because the sides down there will beat you - as the games at Bolton (a 3-1 defeat) and Sunderland (a 1-0 loss) showed.
"If you don't turn up and compete against these sides you will get beat.
"With the players we've got we should be higher in the league - it's as simple as that.
"But we need to go on a winning streak otherwise we'll find ourselves in a position in the league that we don't want."
Goalscoring has been a major source of frustration and the three without reply against Everton took their tally to just 33 in 28 league matches.
While they have been relatively sound at the back, not scoring has put pressure on the defence and that has cost them in recent weeks.
"Defending well gives you the base to go on and create chances and we have been creating chances all season," said Gerrard.
"You can talk about luck and things not going your way but we have to take responsibility to put the ball in the back of the net.
"But unless we can get that ball in the back of the net and have an end product we are going to find ourselves sixth or seventh in the league and that is not what we want."
Having seemingly put their league campaign back on track next up for Liverpool is an FA Cup quarter-final at home to Stoke on Sunday.
After winning the Carling Cup at Wembley last month, the club's first trophy in six years, Gerrard is keen to make a swift return to the capital.
"It is a massive game. We have to treat it like the cup final," said the England midfielder.
"We need to put in a massive performance because we want to take the supporters to Wembley for a second time (this season)."