Though the gunman did not get into the building in Wednesday's attack, he killed two bystanders in a subsequent live-streamed rampage, which appeared to be modelled on last year's gun attack on a New Zealand mosque.
"If police had been stationed outside the synagogue, then this man could have been disarmed before he could attack the others," Josef Schuster, president of the council of Germany's Jewish community, told Deutschlandfunk public radio.
Most Jewish institutions in Germany's large cities have a near-permanent police guard due to occasional anti-Semitic attacks by both far-right activists and Islamist militants.
In a video of more than 30 minutes that the attacker livestreamed from a helmet camera, the perpetrator was heard cursing his failure to enter the synagogue in the eastern German city of Halle before shooting dead a woman passer-by in the street and a man inside a nearby kebab restaurant.
Two other people were injured but regional braodcaster MDR said their condition was not critical.
Police said they had detained one person, identified by the magazines Spiegel and Focus Online as a 27-year-old German, Stephan Balliet.
Schuster said that while it was normal practice in his experience for all synagogues to have police guards while services were being conducted inside, this appeared not to be the case in the state of Saxony-Anhalt, where Halle is located.
However, the head of Germany's police union was skeptical about the feasibility of providing that level of protection.
"We'd have to guard every synagogue, every church, every mosque, every holy place in Germany around the clock, so I don't know if this was a mistake or if this really couldn't have been foreseen," Oliver Malchow told public television.
In the event, the synagogue's solid locked gates and high walls provided ample protection against the attacker's seemingly improvised weapons.
Malchow also defended police in Halle who took 15 minutes to reach the synagogue, saying they could only respond after receiving reports about the incident, and that armored units often had to come from greater distances.
"This shows how thin the level of police coverage is," he said. "Nobody is holding back ... it probably wasn't possible to be quicker".