A poor run of form at the end of the first half of the season saw Dortmund drastically lose ground to Bayern Munich in the title race, dropping to 12 points off the pace at the mid-season break having been just one behind on November 2.
Bayern have gone on to build a 20-point advantage at the top, having won all bar three games in domestic competition this season - Dortmund the only side to beat Bayern in German competition thanks to a 4-2 win in July's DFL-Supercup.
And Klopp acknowledges that shortcomings in Dortmund's performances have cost them dearly.
"We felt that there were games this season in which we would have been better to play football," he said on Friday.
"We're not satisfied with second place."
Klopp expects another tough test when Dortmund face Freiburg on Saturday, especially as star striker Robert Lewandowski is unlikely to be available for the trip.
"Freiburg will want to show that they belong in the division," he added. "It has not been easy for them with the (UEFA) Europa League.
"They have made good games in the last few weeks but were not rewarded.
"Lewandowski's doing well, but it remains to be seen whether he'll be included. There was a slight stretch, (but) the knee is stable and he is pain-free.
"(However) it's not a gamble I'm about to take."
