Sydney chief executive Matthew Pavlich led the tribute as both teams came together before the AFL season opener between the Swans and Carlton on March 5.
But there was no direct mention of the Jewish community in Pavlich's speech, with references allegedly removed after being included in a previous version of the script.
Pridham addressed the issue during the chairman's function before the Swans' round-one clash with the Brisbane Lions on Saturday night.
"I am grateful to journalist and former Swans star Gerard Healy, who called me yesterday to make me aware that our on-field tribute neglected to specifically name the Jewish community as the target of the Bondi shootings," Pridham said.
"This was not intentional. We apologise for this omission. It was a Sydney Swans initiative, and a Swans-led event, and we take full responsibility.
"The tribute was a genuine attempt to show compassion to everyone impacted by the terrible events on 14 December, and most of all the Jewish community."
A prominent media commentator, Healy alleged on Friday the initial script had been changed to remove the word "Jew" and references to the "Jewish" community.
On Saturday, AFL chief executive Andrew Dillon reinforced his support towards the Jewish community during a series of radio interviews, but failed to clarify if the league played any role in the alleged change of script.
"I don't know the ins and outs of scripts," Dillon said on SEN.
"Matthew (Pavlich) did a great job of hosting that ceremony.
"It was the appropriate forum, and it paid tribute to the victims of a horrific attack on the Jewish community."
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