The current Bundesliga champions had to come back from behind after Mainz took the lead with a goal by Nicolai Mullier.
Ivan Perisic and Lukasz Piszczek saved Klopp's side from defeat by sneaking a 90th minute winner from the Polish right-back, and the manager was pleased with the result.
"These were three big points today. I was pleased with the late goal because that it was the least that we deserved," the 44-year-old said to his club's official website.
"We can play as a team and play in our style but it becomes difficult when you are not picking up the right results."
Mats Hummels echoed his Klopp's sentiments in his belief that his side deserved the victory.
"If we had not taken the three points, it would have been undeserved. The game had plenty of pace from both sides but in the second-half we showed that we can still play well," he added.
Dortmund will next play against Marseille in the UEFA Champions League.