Boss Brendan Rodgers admits Liverpool must win their last five games to reach the Champions League.
A 0-0 draw at The Hawthorns put a major dent in the Reds' top four hopes.
They moved into fifth but were six points behind Manchester City in the Barclays Premier League, ahead of the defending champions' home game with Aston Villa on Saturday evening.
Boaz Myhill denied Philippe Coutinho and Jordan Henderson while Jordon Ibe hit the bar as Liverpool improved after the break.
They needed Simon Mignolet to save from James Morrison and the bright Callum McManaman to ensure a point and Rodgers conceded they need a faultless finish.
He said: "It'll be very difficult, I felt of the six games we certainly needed to win five at least so now we have five to go and we'll have to look to win them to give ourselves a chance.
"You never know what happens above you, that's the thing with football, but what you have to do is make sure you keep the pressure on.
"This is a difficult place to come, Tony's teams are strong, we have got a point and now we look to our game in hand in the week (against Hull) and look to get three points there."
Mario Balotelli made his first top flight start since November but made little impact and Rodgers insisted Liverpool will look to buy a new striker in the summer.
He said: "We will look at it in the summer and it's somewhere we will have to do some work on. I give credit to the players because they came out after a difficult result and performance last week (a 2-1 FA Cup semi-final defeat to Aston Villa) and showed great confidence.
"They defended well and attacked with all the invention and creativity as we possibly could.
"We just don't score as many goals, it's as simple as that. The players have given the same effort and attitude but we had two players last year (Luis Suarez and the injured Daniel Sturridge) who played in the front three who got 50 plus goals and we don't have it now."
West Brom are three points from the 40 point safety target set by Tony Pulis but still face Manchester United, Arsenal and Chelsea in their final four games.
They are seven points above the relegation zone and boss Pulis is still wary of being dragged down.
He said: "It's a great point for us and it's something we deserved in terms of the effort we put in.
"We need to keep going, four games and we need to pick points up. Leicester have four straight wins and no-one saw that coming. I have been in this game long enough to know strange things happen at this time of year."
Source: PA
