Which of Klopp's teams was notorious for that? Notorious for burning out towards the end of a match - yes - but not of the season.
The only season they might have gone slower in the Bundesliga at the end of the season could have been 2012/13 when they reached the CL final and Bayern won the Bundesliga title very early. But 10/12, 11/12, 13/14 and 14/15 they had strong last weeks. They usually lost their points on Bayern during the weeks in all competitions - not when they only competeted in only one.
But - I looked into Liverpool's data today and for me it was pretty surprising. They play about 100 more passes a match than Dortmund did, have higher ball possession and passing quotes than Dortmund did - even in their best years. The data looks like Klopp changed his philosophy a little now, too - and mixes ball possession with counter attacking much more than he did before.