The Merseyside outfit tried to bring the Ukrainian to Anfield before the close of the transfer window last Friday, but failed at the final hurdle.
Reports emerged claiming that Dnipro's owner refused to sign the paperwork in order to complete the move on deadline day.
Lawrenson wrote in The Mirror: "I'm sorry but you cannot prostitute your club because the owner of an outfit in the Ukraine decides he wants four or five million quid more. No chance.
"People can point to Liverpool missing out on Mohamed Salah, but Chelsea were always in the background.
"With Konoplyanka I can't really see what more Liverpool could have done. Dnipro were the big losers out of all that carry on. Not Liverpool."
The Reds are currently fourth in the Premier League table.