Additional health and safety measures had let to the £120 million masterplan, which aimed to transform the area, costing £11.4 million more than planned.
But Councillor Louise Miles said the extra cash, which was signed off by council chiefs, was an "increase in budgetary provision" rather than the project going over-budget.
It came as part of a raft of housing investment across the city, which included a new £13.7 million scheme to improve fire safety measures.
Councillor Miles, cabinet member for resources, said: "I'm proud, on behalf of my group and behalf of Councillor Peter Bilson, to draw councillors' attention to the priorities of the programme.
"In addition, I am proud to be able to draw attention to our commitment to our housing stock – including in Heath Town."
Windows in the tower blocks were replaced after showing signs of deterioration, with the cladding – which was already compliant – upgraded in a bid to reduce long-term costs and reduce disruption.
The cost over sprinklers being installed into tower blocks, new lighting and CCTV, have pushed up the cost.
And deck-access blocks on the estate have been upgraded with the fitting of “enhanced” fire doors inside the homes.
Councillor Wendy Thompson, leader of the opposition, said most people would have a "heart attack" if they found out their extension would cost millions more.
She said: "It's an overspend, not an underspend – and if safety measures were not taken into account, then there's something extraordinarily wrong.
"We know sometimes there are some extra costs but not to the tune of millions of pounds.
"It's very easy to spend other people's money and not be accountable – you have a big costings problem and we, on this side, want to get you do so something about it."
Councillor Ian Brookfield, leader of Wolverhampton Council, called on the opposition to vote the motion down if she disagreed.
"If you are so against us spending out on sprinklers, fire doors, retardant materials, then vote this down because that's what you're saying.
"We're spending money because we don't want people to die – remember Grenfell? People didn't spend the money and to be really honest, the Conservative Governments didn't gave a toss about people who lived on their estates.
"But we do – we're happy to spend the money."