Mr Storer, aged 21, from Tamworth, got into difficulty after he went into the water to help a nine-year-old girl out of the reservoir.
Emergency services attended at around 6pm on Sunday but Mr Storer was recovered from the water a short time later.
In a tribute to Carl, his family said: "You were a really good brother and you will be deeply missed by family and friends.
"Rest in peace and fly with the eagles. You will always be loved."
A passer-by went to rescue the young girl from the water but revealed his sorrow at being unable to save Mr Storer too.
Thomas Vale, a 24-year-old care assistant from Shelfield, near Walsall, was one of the first to spot the pair in trouble and immediately jumped into the water to try to help.
He said he was still in shock after the fatal incident and still “couldn’t think straight”.
Meanwhile Staffordshire Police have since urged anybody with video footage of the incident to share it with the force instead of publishing it on social media.
Detectives believe members of the public may have recorded the incident on their smartphones as it unfolded.
Detective Inspector John Quilty, senior investigating officer, said: “It is important that we get answers for Carl’s family and video recordings of the incident would be a huge help.
"I would ask that anyone who did capture footage of the incident refrains from sharing it on social media and instead contacts us for our detectives to view.”
who said officers are preparing an investigation report for the coroner,
Warning to swimmers
Extra police patrols will be made around Chasewater as councillors advise people of the dangers of swimming in open water.
Sergeant Fay Mills, from Staffordshire Police, said: “Carl’s family are receiving support from specially-trained officers and our thoughts are with them at this time.
"We are working with partners to establish the circumstances of his death and a report is being prepared for the coroners.
"We have an increased officer presence at the park today to offer reassurance and we would encourage everyone to avoid swimming in open water for their own safety.”
Staffordshire county councillor Mark Winnington added: "Everyone is upset to hear the news of the tragic event at Chasewater reservoir and it is so sad that a day out enjoying the summer sun has ended in tragedy for this young man and his family and our thoughts are with his loved ones today.
“Though we do not yet know the full circumstances of how this happened, it is a sad reminder of how even the strongest swimmer can find themselves struggling while swimming in cold water.
“We all want to enjoy the warmer weather, but our advice to everyone is not to be tempted to cool off by swimming unsupervised in open waters.”
The warning came as children were spotted playing in the reservoir on Monday just hours after the tragedy.
Staffordshire Police say a number of people were seen filming the incident as it unfolded. They urged people to not share the footage publicly as it may be of a distressing nature.
Anyone with footage is instead asked to call the force on 101 quoting incident number 654 of 30 June to submit it.
Floral tributes have been left at the scene and messages of condolence have been posted on social media.
An online fundraising campaign is under way to support Mr Storer's family.
To visit the fundraiser head to this Facebook page.