Leverkusen were up 2-0 after goals by Jeremie Frimpong and Alejandro Grimaldo but let the advantage slip as Kevin Kampl pulled a goal back for Leipzig in first-half stoppage time and Lois Openda added a brace following half-time.
"We'll take a lot of positives and negatives from this game," Alonso told a press conference.
"We played a good game in the first half. We were happy with that and wanted to build on it in the second. (But) We had no control in the second half and gave Leipzig too much space. We didn't do well in the back line.
"We will learn from these mistakes. It's not good to let an opponent come back after leading 2-0. But it's a process, we're still early in the season."
Leipzig snapped Leverkusen's 35-game unbeaten streak, leaving them one result away from matching Hamburg's tally of 36 games unbeaten in 1982/83 - Bundesliga's second-longest run after Bayern Munich's record of 53 under Pep Guardiola.
"We were in a good flow after taking a 2-0 lead, but we then have to be ready to defend," Alonso added.
"We want to attack together, but we also have to defend together. We'll work through the game after the international break."
Leverkusen were the better side and could have gained a bigger advantage before the break with early chances through Edmond Tapsoba and Piero Hincapie, the latter hitting the bar with a header.
"Of course it hurts because we didn't take our chances today," said Frimpong, who gave Leverkusen the lead on the night.
"In the end we lost because Leipzig took their chances better. It was a good game, but we have to score goals. We will continue to work on that in training."
Leverkusen next visit Hoffenheim on September 14th before travelling to Feyenoord for their Champions League opener five days later.