In a statement on Friday, Brennan said: “We respect the outcome of the election and the message voters have sent. Now is the time for us to reflect carefully on the result, listen to residents, and rebuild trust and support with our communities.
“For that reason, our group will not be entering into any coalition agreement or power-sharing arrangement with other parties.
“We will continue to serve residents constructively from the opposition benches, holding the new administration to account where necessary while supporting decisions that are in the best interests of the city and its residents.”
Councillor Shuranjeet Singh was named the new Labour group deputy leader.
No party was able to secure a majority last week and on Wednesday the Greens ruled out a coalition with Reform, who took 23 of the 101 seats.