Built in 1937, the concrete structure was the "last fragment" of the derelict seaside lido used for the street artist's "Bemusement Park" exhibit last year.
Conservationists said they had been told the fountain, in Weston-super-Mare, would be spared from destruction.
But North Somerset council said it was demolished due to its poor condition.
Visitors to Dismaland were greeted by the sight of the fountain upon entering, and it was picked out by a spotlight at night.
Its dilapidated appearance, however, was not the work of the elusive Banksy, but rather a truck which hit the fountain after the site became derelict.
The impact caused the upper cascade to tip over, leaving it sitting on its side atop the bottom part of the structure.
Weston Civic Society chairman Howard Smith said he felt "angry and upset" the fountain had gone.
"They [the council] gave us an assurance at the end of last year that it would be conserved," he said.
Mr Smith said the fountain survived the building of the Tropicana at a time when the original diving stage was destroyed.
"It was the last fragment of the actual bathing part of the original Art Deco pool.
"It was a beautiful object and it would not have taken much to erect it in another part of the town."
Work to turn the site into a space for arts and performances has been taking place since the end of 2015.
A spokesman for the council, which owns the site, said: "The top of the fountain was dislodged, the surround of the base was broken down and could not be used as a water reservoir, the main stem had numerous cracks in the structure and the edges on the lower main tier were damaged.
"Given its condition, the decision was made to take it down and demolish it."

Eddie Jones' side go into the Six Nations match looking to equal New Zealand's world record of 18 straight Test victories.
However, Cotter says Scotland have enough attacking threats in their ranks to take the game to England.
"The players are keen when they get their hands on the ball to express themselves at Twickenham," said Cotter.
"I think that's a good attitude to have and attitude will determine a big part of the game.
"We know when we defend we'll have to defend resolutely."
Scotland sit third in the Six Nations table, having registered wins over Ireland and Wales either side of a narrow defeat by France in Paris.
The Scots, though, have not beaten England since 2008 and have the unenviable record of not winning at Twickenham since 1983.
Hamish Watson replaces the injured John Hardie in Scotland's only change from the win over Wales.
England have named the returning Billy Vunipola on the bench for Saturday's match, and Cotter admits the powerful Saracens number eight is just one of many strong options Jones can call upon late in the game.
"They [England] have a formula that is working well for them," said Cotter, who will be replaced by Gregor Townsend as head coach at the end of the season.
"They have a bench that is coming on and finishing games off in the last 10 minutes. It's something we're aware of.
"I think they'll comfortably move through the gears as the game goes on and finish in top speed and we've got to stay with them.
"We know more or less what's coming and it's just a matter of withstanding that."
Jones suggested in the aftermath of England's win over Italy that Scotland would be under increased pressure going into the Calcutta Cup match, with expectations raised among supporters after the wins over Ireland and Wales.
"Coaches have different characters and styles," added Cotter. "That's his and everybody has their own.
"I think Eddie's good fun, he's good company. I like having a chat with him outside of the game and in the game we both like to compete as best we can.
"Our players know they're going to have to give their best performance. During that 80 minutes we'll have to string together a number of excellent plays in attack and defence and to think clearly to get them to start adapting to our play.
"It hasn't been discussed a lot within the team, the Calcutta Cup, Triple Crown, nothing. All that has been discussed is content of the game and getting the content right. That's all this team is doing. Nothing else is being applied or talked about."
The demolition of an Art Deco fountain which featured in Banksy's Dismaland show has been slammed by campaigners.
[NEXT_CONCEPT]
Head coach Vern Cotter insists Scotland are not going to Twickenham to merely try to contain England.