It was Liverpool's first win in the group this season, and although they weren't made to work hard for the result, Klopp will be pleased with the ruthlessness his side showed, along with a welcome clean sheet.
Liverpool's profligacy sparked criticism of Klopp's failure to buy a top-class striker and, irritated by questions about his trophyless two-year reign, he sarcastically labelled himself a "charismatic, amusing loser" earlier this week. Mohamed Salah, Philippe Coutinho and Roberto Firmino carry the attacking threat. "We need to be strong and concentrated against a typically, top European team". Two points from their opening two group matches was not what boss Jurgen Klopp would have expected, especially after surrendering a winning position late on at home to Sevilla in their opening game.
Maribor's only real chance came from a set-piece, as Marko Suler was given too much space from the ball in, but headed high and wide for the Slovenians. This time a Coutinho free-kick from wide was glanced on by Firmino into the far corner for his second of the game.
This is the first competitive match between Liverpool and Maribor, who have a poor record in both the Champions League, and against English opposition.
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Second half strikes from Firmino, Alex Oxlade-Chamberlain and Trent Alexander-Arnold wrapped up the contest.
On Tuesday, October 17 at 21:45 in Maribor at the stadium "Ludski Wirth", Maribor will take Liverpool in the match 3 rounds of the Champions League.
Klopp was all smiles on the touchline and there was still time for teenage defender Alexander-Arnold to net in stoppage-time with a deflected long-range effort.