Spurs were sent crashing out by a brilliant Mislav Orsic hat-trick as they blew a two-goal lead from the first leg.
Asked how the players were feeling after their humbling, the goalkeeper pulled no punches, saying: “Good question. I think we are all more than disappointed.
“It's just a disgrace. I just hope everyone in the changing room feels responsible for the situation, because it's a disgrace.
“What more can I say about it? Talking about the game from Sunday, I think it is not the right moment.
“Just the taste of the defeat tonight is more than painful and we are all responsible for that.
“Obviously we are a club which is full of ambition but I just think the team at the moment is a reflection of what's going on in the club."
Lloris said Tottenham had been punished for failing to master the basics - and for underestimating their opponents.
“We have a lack of basics, lack of fundamentals and all our performance is just in relation to that," said the France international.
“I think mentally we should be stronger, we should be more competitive. Today, I didn't feel that on the field, unfortunately.
“When you are not ready at this level you pay straight away.
"It doesn't matter who the opponent is, there is quality everywhere in the Europa. If you don't respect the opponent it's kind of permission and that's what happened today.
“Full credit belongs to the opponent as well because they played the game full of belief, but the blame is on us, all the team, all the club. We are guilty."
Asked to expand, he added: “I don't have to go deeper. I mean it's not possible.
“The way we play is just not enough, not enough. It's one thing to come in front of the camera to say we're ambitious, the other is to show it every day in training sessions, to show it every time on the pitch.
“You cannot let it down, if you play or don't play. To behave as a team is the most difficult thing in football, whatever is the decision of the manager you have to follow the way of the team.
“If you follow the team only when you are in the starting XI, that causes big problems for the team because you pay in one moment and you're going to pay in your season.
“Today I think is the consequence of that. We had great moments in the past because we could trust the togetherness that was in the team.
“Today, I'm not sure, I don't know about that."
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