The England international joined West Ham United on a season-long loan deal with only one day left to go in the summer transfer window.
Luis Suarez and Fabio Borini are now the Reds' only recognised strikers after the club failed to bring in another forward, and Nicol is shocked by his old club's dealings towards the end of the transfer window.
"Liverpool should have kept hold of Andy Carroll," Nicol told talkSPORT.
"If Brendan, or whoever is making the decisions at the club, has let Andy go then you must have a replacement all done, dusted, signed and sealed.
"Otherwise you are left with a situation that they find themselves in now. It's a horrendous decision and it could really cost them. If Luis Suarez gets injured, I have no idea who will play centre-forward."
Liverpool have yet to win a Premier League match this season.