George Redmond insisted he has it "in writing" that residents would not be affected by the changes until shortly before midnight on Sunday.
However, he claims some people in Dalmarnock were told to move their cars on Friday.
As reported in later editions of last night's Evening Times, other residents were woken early on Sunday to be warned of restrictions.
Calton councillor Mr Redmond held talks with Glasgow 2014 organisers over the parking restrictions and a proposed event for residents after the games, which could see Glasgow-born rockers Glasvegas play a homecoming gig in Dalmarnock.
Mr Redmond said: "They have brought the restrictions in early, without any notice.
"I'm becoming increasingly frustrated by the organising committee. They agree something then they change it without notifying you. It's unacceptable and I think there are serious issues about the organisers' competence."
Residents with special permits must display them in their cars between July 7 and August 6 to comply with strict security measures.
Cars without the pass can be lifted to protect residents' parking from spectators.
A Glasgow 2014 spokesperson said: "All restrictions have been communicated to local residents.
"Residents requiring a Restricted Access Parking Permit (RAPP) have had individual visits from Police Scotland, advising them of the measures.Residents who require Event Day Parking Zone (EDPZ) permits will receive them over the coming week."