The Reds followed up their first-leg victory with another impressive display to move into the quarter-finals of the Champions League with a 4-0 aggregate win in Budapest.
And Thiago shone in the middle of the park, showing his supreme quality after a difficult first season in England.
Speaking after the match, Klopp said: “I assume when you all look at Liverpool from Germany, people say [our problems are] to do with Thiago or whatever – that's rubbish.
“Thiago was good, they were all good. For the players who were new, they always needed time to get used to our gameplan, but Thiago doesn't have that.
“Still, he improves week on week. It's not a short-term project, it's a long-term project and it was good.
“It is very fluid how we work together. The boys played some nice passes and Thiago had a great chance as well. I think he could have had a shot on goal but instead passed.”
Perhaps the Spaniard’s highlight of the match came in the first half when he produced a remarkable scissor kick half-volley to set Mohamed Salah away, only for the Egyptian to see his effort saved.
Although they were not playing at Anfield due to coronavirus restrictions, Liverpool’s win last night will technically go down as a home victory.
And so it ends a run of six home defeats in a row, a remarkable sequence of results which has seen them slip to eighth in the Premier League table.
The English champions sit seven points off the top four, meaning their best route into the Champions League next season could well be to win the competition.
Liverpool join Porto, Borussia Dortmund and Paris Saint-Germain in the last eight after the French side knocked Barcelona out to make this season the first time since 2004/05 that neither Lionel Messi or Cristiano Ronaldo will feature in the quarter-finals.
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