(CNN) -- Alameda, California, has immediately changed its policies after first responders watched a man drown in San Francisco Bay and did nothing to rescue him.

The man was apparently suicidal, CNN affiliate KTVU reported. After he entered the bay off Alameda Beach on Monday and stood in neck-deep water, then treaded water, police and firefighters who were called to the scene did not set foot in the bay.

The events of Memorial Day were "very difficult and very regrettable," Alameda Interim Fire Chief Michael D'Orazi told CNN Wednesday.

Two things prevented authorities from taking action, he said. First, because it was a crime scene, the police department was in charge. "They felt that going into the water initially might not be the best idea because they were unsure if this individual was armed, the stability of the individual," D'Orazi said.

Also, "there was a policy in place that pretty much precluded our people from entering the water."

That has been changed, he said. "We will be putting into effect a new policy which allows our commander discretion after these circumstances."

The firefighters on the beach "were incredibly frustrated by this whole situation," he said, adding that "they wanted to get in, they wanted to take action."

Local officials said that because of a lack of funding for shore-to-water rescue, firefighters had no one properly trained to go into the water, KTVU reported.

"It's muddy out there. We don't want them sinking. We don't want them in distress," Alameda Interim Police Chief Michael Noonan said in the KTVU report.

One local resident, addressing officials at a meeting about the incident, said, "It just strikes me as unbelievably callous that nobody there with any sort of training could strip off their gear and go and help this person."

In the interview with CNN, D'Orazi said that if firefighters had chosen to enter the water despite the policies, he "wouldn't have an issue with that." But the situation should not recur, because the policies have been changed, he said.

News reports said a woman ultimately tried to save the drowning man, but was too late, and ended up pulling his body to shore.