BVB won on Tuesday night 3-1, thanks to Serhou Guirassy's hat-trick, but lost the Champions League quarterfinal 5-3 on aggregate.
Kovac said afterwards: "It was important to score the first goal almost straight away, then after the second I thought that if we held out we could do it but there was this own goal, with the third anything could have happened.
"But I'm happy with what the team did."
Asked if he was more disappointed by the defeat in Barcelona or satisfied by this victory, Kovac added: "Of course we were disappointed by the result in Barcelona, because we didn't play well, but I'm happy with what we showed tonight.
"We have quality, we have to prove it game after game."
First-leg regret
Meanwhile, Guirassy also admitted mixed emotions.
He said, "A great night for the fans and for me too, we beat a great team but it's a shame to have lost 4-0 in Barcelona.
"Today we showed that we can play great games, we hope that the defeat in the first leg will help us in the future".