SDLP leader Colum Eastwood has said there had been cross-party understanding that someone from his party would become the new Speaker of the assembly.
But he said an hour before Saturday’s assembly sitting, Sinn Féin put Alex Maskey forward for the role.
“It wasn’t the best start,” Mr Eastwood told BBC Radio Foyle.
“We have never had the Speaker’s position, and we felt it was right … the SDLP had it this time.”
He added: “And of course the DUP supported it. That’s fine but I just thought that was a missed opportunity.”
However, Mr Eastwood said the election of speaker was “a minor issue compared with what this government has to do”.
In response, Sinn Féin said “there was no ‘loose’ or any other agreement that Patsy McGlone would be assembly Speaker”.
The DUP’s Christopher Stalford; UUP’s Roy Beggs and Mr McGlone have been elected as Mr Maskey’s deputies.
The North’s Assembly sat on Saturday for the first time after three years of deadlock.