The Reds meekly exited the Champions League after a 1-0 (6-2 on aggregate) loss to the holders in the last 16 tie and Klopp knew that his team did nowhere near enough to overturn the three-goal deficit from the first leg.
The Liverpool boss said: “In moments it was a good performance but Real Madrid were the team in control for most of the game. They had the better chances.
“Ali (goalkeeper Alisson Becker) had to make two sensational saves to keep us in the game and that’s the reason (we lost).
“If you want to get through, you need to be outstanding. If you want to win the game, you need to be really good, and Madrid was the better team and that’s why the right team went through to the next round."
The defeat ended Liverpool's hopes of winning a trophy this season and Klopp has urged his players to "squeeze absolutely everything" from a frustrating campaign by securing qualification for the Champions League next season.
The German coach said: "Our job is to squeeze absolutely everything from this season as possible.
"It's a strange one so far, just our recent two games, a sensational performance against Man Utd, a very good football team, and a really bad performance against Bournemouth, again a good football team, but we should not lose this game.
"That put us again under more pressure. Three points, and I think everyone would have really felt it, smelt our breath if you like."