Meir Facto, executive director of Shomrim, also expressed disappointment that the organisation had not been consulted during the process.
He said the voluntary safety patrol, which works with Greater Manchester Police, had a longstanding role in community cohesion efforts.
“Building trust, strengthening relationships between communities and creating safe environments where people feel connected and supported are all essential elements of preventing division and promoting community resilience,” he said.
Responding to the criticism, a spokesperson for Salford City Council said it recognised the “profound impact” of the attack on Jewish communities.
The spokesperson said the authority stood “in solidarity” with the Jewish community and that the funding would be used to tackle antisemitism and promote understanding between different communities.
“We understand the concerns that have been raised and will continue to engage to ensure the experiences and priorities of our Jewish communities are reflected in the wider community projects we undertake,” they added.