The Reds eked out a 2-1 victory over Southampton on the opening day of the Premier League season, but the feeling remains they have not adequately replaced Luis Suarez yet.
The Uruguayan joined Barcelona in a £75million move earlier this summer and while many agree he is impossible to replace, Liverpool has only brought in two strikers this summer - veteran Rickie Lambert and Divock Origi, who is spending this season back on loan at Lille.
Brendan Rodgers said after the Saints win he was still looking to strengthen his squad and Beecroft believes up front must be a priority.
"Liverpool do need another striker. Brendan Rodgers is saying 'well we’ll have a look but if we don’t get another striker in this window, then there’s no panic'. Believe you me, Liverpool need a striker before the window shuts otherwise they will be in trouble as far as the season is concerned," he told Extra Time.
"It only needs an injury to Daniel Sturridge and/or Rickie Lambert and they will be in trouble, there is no question about it.
"They need quality in there. I think they’ve got the money to buy quality, it’s just a question of whether they can persuade their targets to come and sign for Liverpool Football Club but it is vital, and I repeat vital, that Liverpool do make that signing before the transfer window closes."
Liverpool saw a transfer for QPR striker Loic Remy fall through earlier in the window after a failed medical, while in recent days they have been linked with a shock move for former Chelsea striker Samuel Eto'o and Reds legend Steve Nicol has encouraged the club to move for Swansea forward Wilfried Bony.
