Goals from Henrikh Mkhitaryan, Marco Reus and Jonas Hofmann helped Klopp's men to a convincing win over champions Bayern - who wrapped up the Bundesliga title in March - at the Allianz Arena.
That result came off the back of a 2-0 win over Real Madrid in midweek, which was not being enough to keep them in the UEFA Champions League.
Despite the disappointment of being eliminated from Europe's premier club competition at the quarter-final stage, Klopp feels the positive effects of beating Real and Bayern - who will meet in the Champions League semi-finals - can help them keep Schalke at bay in the race for second place in the Bundesliga.
Three points separate Dortmund from their rivals, and Klopp is eager to cement the runners-up spot after taking what he described as "bonus points" against the Bavarians.
"These three points do us a lot of good. As points against Bayern Munich are like bonus points for any team," he said.
"I'm very happy that we were able to snatch three of them.
"In the end, it was an exceptional week in which we managed to beat Real Madrid and Bayern Munich - and that in a fantastic fashion.
"Bayern may have lacked a bit of focus after already claiming the title, but we came here with a plan and were able to implement most of it. It was hard work, a lot of hard work."
Klopp opted to leave Bayern-bound Robert Lewandowski on the bench for much of Saturday's fixture, and the coach revealed he allowed his side a restful few days after their exertions against Real and ahead of Tuesday's DFB-Pokal semi-final with Wolfsburg.
"We left the team alone for three days after the game in Madrid and only started our preparations for the Bayern Munich game (on Saturday)," he said.
"For us, a game against the best team in the world is always the game of the year, and that’s why it didn't cross my mind that I could leave anyone out of it.
"(Lewandowski) is our most-used player, while (Lukasz Piszczek) was out injured for half a year and also needed a break.
"And Mats (Hummels) decided himself that he wanted to play."
