Karius gifted Madrid two goals in Kiev as Liverpool fell to a 3-1 defeat to the now 13-time European champions, first throwing the ball against Karim Benzema and then fumbling a long-range Gareth Bale strike into his net.
Lawrenson admitted that he felt sympathy for the German, but believes that his performance on the biggest stage proves that he is not good enough to be Liverpool's number one.
"I feel sorry for Loris Karius, because he will be absolutely heartbroken after his nightmare display in the Champions League final - but I don't see any way back for him at Liverpool now. Karius had an awful night and it was horrible to watch the Reds goalkeeper completely alone in his penalty area at the end of the game. The Real Madrid players were the first to console him, followed by a member of the Liverpool coaching staff," Lawrenson told BBC Sport.
"I know from experience that when you lose a big game as a player, you sometimes need a few minutes to collect your thoughts, and those are times you are really just thinking about yourself. But surely one of his teammates could have gone over, put their arm round him and given him a big hug - even if they did not know what to say.
"I am sure they did that back in the dressing room, once they got over their disappointment, and his manager will have a quiet word and support him too. But, even if Klopp backs him publicly as well as privately, he must know that he is not good enough for Liverpool and what they want to achieve.
"You need a top goalkeeper to win trophies and he is not one of those. Can they afford to keep playing him, thinking he might become one? No. Karius always looks like he has a mistake in him, and that cost them dearly on Saturday night."