It was a night to forget for Bayern at Allianz Arena, where the Bundesliga champions suffered a 3-1 second-leg defeat to Liverpool on Wednesday.
Following last month's scoreless stalemate on Merseyside, Bayern were no match for Liverpool – who condemned the German giants to their earliest European exit since 2010-11.
Speaking afterwards, Kovac told Sky: "We had a strong opponent and we have to congratulate Liverpool and Jurgen Klopp.
"They were better in these two matches and we deserved to lose. The opponent attacked us very high and left no spaces, that made it difficult for us.
"On top of that it was not our best day. Liverpool are a top team in Europe and they showed us our limits."
He continued: "You saw after the second goal how much quality they have.
"We still have two titles to fight for. We're top in the Bundesliga and we're still in the cup. Our goal is to win both of these competitions."
Bayern conceded first at home, with goalkeeper Manuel Neuer caught out on the edge of the penalty area as Sadio Mane put Liverpool ahead in the 26th minute.
A Joel Matip own goal 13 minutes later restored parity for Bayern, however, the hosts were swept aside in the second half as Virgil van Dijk and Mane led Liverpool into the quarter-finals.
Asked about his involvement in the opening goal, Neuer said: "I wanted to stand right ahead of Mane, but his first touch was superb. If he does not control it perfectly, I am there [to take the ball]. Then he makes a great move.
"If I stay on the line he can run at me one on one. I can see why people think I did not look to good. Still, Mane did it really well."
Meanwhile, Bayern defender Mats Hummels credited Reds boss Klopp as the architect of the German giants' downfall.
"I know Jurgen Klopp and he is very good at eliminating the opponents' strengths and he showed that again today," he said.
"The 1-2 took away our belief. After that Liverpool was the better team. Still this was not a great game of football."