A police officer tried to punch through the ice as he and others attempted to rescue the children in Babbs Mill Park, Kingshurst, on Sunday.
A fourth boy, aged six, remains in a critical condition in hospital after being pulled from the icy water.
Family members affected by the tragedy are “absolutely devastated”, said Supt Richard Harris of West Midlands Police.
Supt Harris said all police who went to the scene had entered the water with no regard for their own safety or with any special clothing – some going in waist-deep.
“One of my officers was trying to punch through the ice to actually rescue the children themselves,” he said.
“That officer, as a result of that, had some mild hypothermia yesterday. I’m pleased to say he’s now been released from hospital and he’s absolutely fine.”
Searches are continuing at the lake and Supt Harris said teams wanted to be “100% certain that there is no-one else possibly in the water at this time”.
“It’s important to stress though that we’ve had no contact from anybody suggesting that there is anybody else missing.”
He added officers were still trying to work through all the details of the incident and could not say how long the boys had been in the water before emergency services arrived.
However, Supt Harris said officers had arrived within minutes of the first call, which came in at about 14:30 GMT.
Members of the public and police officers initially went into the freezing water to try to get the youngsters out, before the children were reached by specialist firefighters.
At the scene, BBC Midlands Correspondent Phil Mackie
Firefighters from Red Watch, at Sheldon fire station – about five miles away from the park – were among those who tried to rescue the boys.
They brought flowers to the scene on Monday.
Onlookers applauded as the firefighters laid them down alongside a growing number of tributes.
The mood remains sombre as the search of the lake winds down.
Temperatures are thought to have plunged to 1C (34F) in the area at the time of the incident, falling to -3C (26F) overnight.
They were rushed to Birmingham Children’s Hospital and Heartlands Hospital, but police said they could not be revived.
St Anthony’s Primary School, in Kingshurst, tweeted it would be closed on Monday “due to the incident at Babbs Mill” and asked for prayers for those affected.
Police said their thoughts were with the families and friends of the boys “at this deeply devastating time” and they would have specialist officers on hand to support them.
Richard Stanton, West Midlands Fire and Rescue Area Commander, described the deaths as “a tragedy beyond words”.
He said the incident served as a reminder of the dangers of frozen water.
“It can look picturesque but can be lethal,” he said. “Please help avoid this from happening again.”