A 3-2 loss to Atletico Madrid meant the current holders were eliminated at the last-16 stage.
But former Reds striker Owen thinks Klopp's men are still the continent's best side.
"Liverpool are out now but there's no question whatsoever that every single big team around Europe has just breathed a huge sigh of relief," Owen said on BT Sport.
"Liverpool are out and I've got no doubts that they're the best team in Europe. Yes, they've been beaten over two legs but they're still the best team in Europe and they were absolutely outstanding for 90 minutes I thought tonight.
"The difference probably between the two sides was the goalkeepers.
"The Madrid players will sit in there dressing room, look at each other and say 'How good were that team we've just beaten? We've never played anything like that'.
"They literally blew them away for 90 minutes but perseverance, hanging in there, and anything can happen in football."