Xabi Alonso wants Leverkusen to be more aggressive after snatching late Bundesliga win
Leverkusen were awarded a penalty deep into added time and Florian Wirtz scored on a rebound to earn the visitors the three points after Gladbach's Ko Itakura fouled substitute Amine Adli.
"It was an intense first Bundesliga game for us. A lot of things happened in the second half, it was full of emotion right to the end. We did well in many phases," Alonso told a press conference.
"But we weren't always so compact today, we were also a bit passive in some phases. We have to do that better. We have to be more aggressive.
"It's difficult to explain why we always score late goals. We can't train that and I can't influence it. It's the mentality of the team."
Champions Leverkusen, who set a European record of 51 consecutive games without loss across all competitions last season, kept their unbeaten streak intact with a number of late equalisers.
"We said at half-time that we must not let up and not think that the game is over," said former Gladbach player Granit Xhaka.
"At the end of the first half, we started not being consistent enough in our passing game and losing easy balls. Here at home, Gladbach never die, you could see that in the (goals for) 1-2 and 2-2."
Xhaka gave Leverkusen the lead in the 12th minute but did not celebrate out of respect for his former club.
"I had the feeling that we made it unnecessarily difficult for ourselves," added Wirtz, who scored two goals on the night, including the decider.
"We were asleep when it came to conceding goals. We let it slip away ourselves, even though we were actually in control, although we didn't have the ball the whole time.
"I just wanted to decide the game. I know that in the end it will be a lucky win. (But) we are happy that we won and that I was able to score the follow-up shot."
Leverkusen came into the game off a German Super Cup win, where they beat VfB Stuttgart 4-3 on penalties after scoring a late equaliser to snatch a 2-2 draw over 90 minutes and lift the trophy on Saturday.