Victories over Jurgen Klopp's former club Borussia Dortmund and Villarreal had carried the Reds to their first European final since 2007 in the German's first season in charge.
Daniel Sturridge's exquisite first-half goal would have been worthy of winning any UEFA showpiece but Klopp's side failed to capitalise and went to pieces in the second half in Basel.
The defeat ended Liverpool's hopes of qualifying for the Champions League, with the Reds finishing eighth in the Premier League.
It was Klopp's fifth consecutive loss in a final, and he said: "There are more important things in life than football. I don't think God had a plan with me to go to the final and always have a knock.
"I've had a lot of luck in my life as I sit here as manager of Liverpool. I don't think I am an unlucky person or life has not been good to me.
"We will carry on, I will carry on. I will try with all I have to reach the next final, even when you know you can lose it. There are bigger problems in life but at this moment it doesn't feel like it, it is really hard.
"We are disappointed and frustrated 100 per cent but tomorrow or later in the week we will see it a little bit more clearly and we will use this experience, that is what we have to do."