The visitors raced into a 4-1 lead but failed to kill off the hosts who then scored twice to set up a nervous finale.
"The second-half performance at times was very good especially when we went two or three goals in the lead," England international Henderson told the club's website on Monday.
"But ... we need to manage the game better especially when they scored the second and gathered momentum. We just need to be a little bit more street-wise."
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Philippe Coutinho's sublime free kick for Liverpool just before halftime cancelled out a 31st-minute opener from Theo Walcott who also had a penalty saved by Simon Mignolet.
"We came in after the first half knowing we could play better," Henderson said. "The manager (Juergen Klopp) said a lot of things we needed to improve on in the second half and I felt we did that."
Three quickfire goals from Adam Lallana, Coutinho and Sadio Mane at the start of the second period established a three-goal advantage for Liverpool.
Klopp celebrated with his players on the sidelines and he took some of the blame for Alex Oxlade-Chamberlain and Calum Chambers reducing the deficit for Arsenal.
"I have a big, big part in the excitement in the last half hour," said the German, "because it's not allowed to celebrate the fourth goal when there is still half an hour to go."
Former Sunderland midfielder Henderson added: "We opened the path for them again. We've got to be a little bit more disciplined at times.
"There are a lot of things to improve on and work on but a lot of good things as well."
Liverpool travel to Burnley for their second league game of the season on Saturday.
(Reporting by Ed Dove; Editing by Tony Jimenez)
