Jurgen Klopp said there can be no denying the right team progressed from their Europa League round-of-32 tie with Augsburg.
The Liverpool manager was delighted with the performance that brought a 1-0 win over the German side after a 0-0 draw at the WWK Arena.
The Reds were wasteful in front of goal but secured a spot in the last 16 courtesy of a James Milner penalty.
Klopp said: "Over 70 minutes we were that good that we couldn't see their plan. Then at the end they had the long balls and could change [Raul] Bobadilla and a few other players, strikers.
"The free-kicks were the biggest challenge for us. But it was a really good game and it was absolutely deserved; everybody who saw the game would have to say we deserved to win and were the better team and created chances.
"We only had one problem - we didn't use them and score often enough. That's how football is sometimes. For us, it's still a long way and the only problem was we couldn't control the game in the last 20 minutes.
"But now, after the game, with a 1-0, I am completely fine. As far as I know, there are no injuries. It was hard, that's how it should be, and now we are in the next round - well deserved."
Klopp reserved special praise for Lucas Leiva - who was the one new starter from the first leg in Germany, replacing Kolo Toure.
The midfielder stepped into the heart of defence alongside Mamadou Sakho and helped the team to a third-straight clean sheet.
"I knew we had to play more football from the last line; Kolo has a lot of quality and skills but the first one is not that he always wants to play," he said.
"Against deep defending we needed in nearly all positions a player who wants to play a pass. Not the last pass from the last line but with passing skills. That was one thing.
"The other thing was that Kolo did really well and played great for us but has a lot of games now in his legs. Lucas was waiting and everybody could see he played this role really well.
"I'm really pleased for him. It's not too easy for Lucas when he doesn't play, he's a different person!
"Everything is OK but it's not easy for him to enjoy life when he's not playing. So he deserved this game and I'm really pleased for him."