Despite defeat at City last week, Klopp was delighted with what he saw.
"From my point of view we were never on a level with City since I came in," said the German.
"We won games against them, especially since Pep, but in these games City were better.
"We only scored more goals, but the possession was at least 60:40 for them in all the games but we won them. Now it was 50:50.
"We had our moments (on Thursday) and caused them completely different problems to the games before.
"Last year the Champions League (quarter-final) game at home when we won 3-0 it was a brilliant game but we were under pressure in a lot of moments.
"I don't know if we had more than four shots on target but we were quite clinical that day.
"That's how you have to play against City, in the moment when you get the ball you have to make the best of it.
"This game was different and that is an important step for us. It is very important we see it."