Look at Klopp in Borussia Dortmund. In the 2010/2011 and 2011/2012 seasons, he won the Bundesliga.
In the 2011/2012 season, he also won the Pokal final against Bayern by 5-2. In fact, he defeated Bayern five times in a row in those two seasons. And Bayern was a great team, who reached the UCL final in 2012, knocking out Real Madrid in the semi-finals.
But look at Dortmund's Europe record in those same two seasons in which they were so good domestically, winning Bundesliga twice, had a good team, and beat Bayern (one of the greatest teams in Europe) five times. In the 2010/2011 season, he was third place in the Europa League group stage, which had PSG and Sevilla, and fell out before the KOs. In the 2011/2012 season (remember, the same season in which Dortmund won the double, and beat Bayern three times, with Bayern reaching the UCL final), Dortmund was BOTTOM of their UCL group, which had Arsenal, Marseille and Olympiakos! An embarrassment!
Europe is different, and even Klopp took some time before learning how to play in Europe, even when he had good squads. Xavi still has to learn.