Fredrik Sjovold scored the decisive goal in the second half as Dortmund struggled to find their rhythm and failed to match the hosts' energy for much of the match.
"We basically weren't in the game until after conceding," Kovac told DAZN.
"In the first half, we didn't play with the passion, intensity or football that we need in order to win."
The Dortmund coach admitted his team improved after making four substitutions, but insisted their overall performance did not warrant a better result.
"It was only after the quadruple substitution that we got into the game better and took control of it somewhat. But up until that point, the opposition were clearly the better team," he said.
"So we can't complain. We deserved to lose the game."
Kovac also accepted responsibility for his team selection after making several changes to his starting line-up for the trip to Norway.
The Croatian insisted his squad had enough quality but was frustrated by the players' failure to show the necessary commitment.
"Ultimately, every single player in our squad has the quality to play. That didn't work today," he said.
"I'm the one responsible for that. I picked the team, but the passion was simply missing today."
Dortmund only raised their level after falling behind, allowing Bodo/Glimt to take control of a contest in which the German side struggled to create consistent attacking pressure.
Kovac was particularly unhappy with his team's use of the ball, arguing that they made it too easy for the Norwegian side to defend.
"We didn't do well at all with the ball today. The opposition were much quicker, much more agile and attacked the spaces in behind much better than we did," he said.
"We played everything into feet, nothing behind the defensive line. If you don't play in behind, you can't stretch the opposition or disrupt their defensive shape."
Dortmund must now respond quickly, with a Bundesliga trip to Union Berlin awaiting them on Saturday.
Paris Saint-Germain manager Luis Enrique has admitted his side were fortunate to beat Manchester City 4-2 after surviving a fierce second-half comeback to maintain their perfect start to the Champions League.
Aston Villa midfielder Ross Barkley praised the performance of this team following the 6-0 victory over Turkish giants Fenerbahce at Villa Park on Wednesday.
Jose Mourinho has criticised the Spanish football authorities over their handling of Vinicius Junior's suspension after Real Madrid fought back from two goals down to beat Roma 4-3 in the Champions League.
Andoni Iraola has praised Liverpool's attacking display after they secured a 6-3 Champions League victory over LASK in Austria, with Bradley Barcola scoring a hat-trick and young midfielder Lewis Koumas opening his European account.
