The Latics were originally the only club in the running for the £125,000 Robins forward, but a late Doncaster bid deterred Moore's side and Heffernan chose to move to Belle Vue.
Moore said: "I'm disappointed about the Heffernan deal, it was awful how Bristol City handled the situation."
But he still hopes to swoop for transfer-listed Sheffield United forward Luke Beckett, who had a loan spell at Boundary Park last season.
He added: "We are still trying to land a deal with Beckett.
"Coming to Boundary Park would be an ideal opportunity for him - last season both he and Chris Killen had a good understanding."