A Bronx jury’s decision to award $183 million in damages to five New York City firefighters caught in a deadly 2005 blaze could face more legal wrangling, as the city’s lawyers criticize the verdict and contemplate an appeal.

The verdict announced Monday by a state Supreme Court jury stemmed from lawsuits filed on behalf of six firefighters who were trapped inside a Bronx apartment building as a fire closed in on them.

With...