Monday's parade was expected to pass through the Campsie and Crevanagh Road areas, but that was changed over concerns a number of flags were put up along the route.
The decision to reroute was taken during a two-hour long emergency council meeting hours before the event was due to begin.
Cllr Sean Begley, of Sinn Féin, said the failure of Unionist representatives to have the flags removed defied the plan for an inclusive event.
"We have been engaged extensively with unionist representatives regarding the proliferation of union flags along the parade route," he explained.
"We made the case that the huge number of flags makes the environment uncomfortable for many nationalists and completely undermines the council's policy of neutrality.
'However, despite this, unionist representatives refused to try and deal with the issue and in light of this we voted to change the route of today's parade to one that is more inclusive.
"It is highly frustrating that unionists like to talk about cultural equality but when it comes to actually showing leadership they fail miserably."
The parade began at 1pm and started from the Grange car park and along the Mountjoy Road, Drumragh Avenue and Market Street on its way into the town centre.
A spokesman for Omagh District Council said the change "followed concerns being expressed about the neutrality of part of the parade route".
But Omagh District Council chairman, Errol Thompson, said it was a "backwards step" for community relations in the town.
"The idea of St Patrick's is it's a day for everyone. We asked them [Sinn Féin] to have 10 minutes of tolerance on this issue but they were not prepared to move on it," said the DUP representative.
He said the decision to have the parade travel along the Campsie Road area was an attempt to make it more inclusive, and all parties were aware that Union flags had been put up on the route earlier this year.
Mr Thompson added that community relations in Omagh have never been better, but Monday's decision could rock the boat.
"The unionist community in Omagh today will be feeling that they have been sidelined," he added.
"I fear for the future of the parade for it being inclusive."