Daniel Brosinski, Jhon Cordoba, Yunus Malli and Yoshinori Muto got the goals as the Bundesliga outfit ran out the deserved winner against the weakened visitor, which made nine changes after playing Barcelona at Wembley a day earlier.
A frustrating day also saw Klopp concerned by an ankle knock for Marko Grujic, who picked up his second injury of pre-season in the first half.
Having convincingly beaten Barca 4-0 on Saturday, only Emre Can and Adam Lallana kept their places for Liverpool, but Mainz had themselves played two midweek games, so made four changes from their 2-0 defeat to Novara.
Unsurprisingly, the visitor struggled to find the same rhythm that had undone the Spanish champion, and after Andre Wisdom was penalised for a handball in the area after 15 minutes, Brosinski coolly rolled the spot-kick into the net.
In the clubs' previous meeting, 10 years earlier, Mainz, then managed by Klopp, had humiliated Rafael Benitez's FA Cup winner 5-0, and the pattern of play here quickly suggested a repeat was not out of the question.
Sure enough, shortly before the break, Liverpool was hit by a double blow as Grujic hobbled off before Cordoba lashed in a second at the near post.
With the Premier League side increasingly careless in possession, it fell further behind in the second period when substitute Malli carried the ball forward to thump past Alex Manninger.
Mainz was not finished there, either, with Klopp wearing a bemused smile as Muto beat his statuesque defence to a cross and nodded in for a fourth.
With a late Danny Ings consolation disallowed, Klopp's men must now look ahead to its Premier League opener at Arsenal next weekend.