The 21-year-old has scored five goals in 11 Bundesliga games since departing the Emirates Stadium in the summer, as well as registering a hat-trick on his senior Germany debut earlier this month.
Gnabry, who saw his progress at Arsenal curtailed by injury before a disappointing loan spell with West Bromwich Albion, insists that the Gunners "badly" wanted to keep him but he had little choice but to seek first-team football elsewhere.
"It was the right decision. Everybody who compares my development over the last four months to my time in England before that can't come to a different conclusion," he told Kicker.
"That was the main reason for the transfer - I wanted to get more playing time and it worked. Arsenal wanted to keep me, badly. But I had to look after my development. If a player does not perform well, a club has no sympathy and they do not want to keep him."
Bayern Munich were the frontrunners to land Gnabry from Arsenal earlier this year, only for Bremen to get in ahead of their German rivals on transfer deadline day.