Former Liverpool star said the club simply did not turn up in the second half.
Speaking to The BBC after the game, Lawrenson observed that during the second 45 minutes, Jurgen Klopp's side did not even have a brief period where they were on top.
He said: "Liverpool had the better of the first half and it was a great goal by Daniel Sturridge.
"But they never started the second half and if anything got worse. They didn't even have a bright spell after the interval - not even five minutes."
Speaking to BBC Radio 5 Live during the second half, Lawrenson described a lack of ability to get on the ball and play their own game, with Liverpool unable to offer a threat.
He noted: "There's nothing we have seen this half that would convince us Liverpool can get back into this. My worry for Liverpool now is who is going to create the chances? Every time Sevilla go forward they are creating chances. There's nothing Liverpool can do about it."
Sevilla have now won the Europa League for three consecutive seasons, and Unai Emery's side produced a top class performance.
Their reward is a place in the Champions League next season, and it will be intriguing to see how far they can go. Liverpool meanwhile will not be playing European football at all in 2016/17.