Council chief executive Sue Bruce insisted that the £776 million estimate of the cost includes a "sufficiently large" risk allowance - and said she does not expect to come back to councillors and ask them to approve more funding.
But she stopped short of giving a guarantee that they would definitely not require more money.
Labour councillors called for the Scottish Government to start a public inquiry into the whole project immediately.
The move came after councillors agreed to reverse last week's shock decision to only take the tram to Haymarket and instead take it as far as St Andrew Square.
Mrs Bruce told the Evening News: "We know there is nervousness and uncertainty because, although we have done all of the things you would expect us to do, when you dig up roads you can find things you don't expect, so we have left an enormous risk pot to cover that."
The estimate includes a 0.8 per cent, or £1.1m, "risk contingency" for off-street work between the airport and Haymarket, as well as a 71.8 per cent, or £30m, risk allowance for the on-street work from Haymarket to York Place.
When asked if members of the public should be confident that more money will not be needed for the project, she said: "They should have faith that £776m is our estimate of the project to St Andrew Square.
"We do not expect to have to come back to ask for more money. We think it is the best estimate we can come to for completing the work."
After the decision was approved, councillors urged the Scottish Government to get on with a public inquiry.
A spokesman for First Minister Alex Salmond said last week that it would happen "once there is greater clarity about the direction of the project".
Cllr Andrew Burns, leader of the Labour group, said: "I do not see why a public inquiry cannot start right away and I would urge the Scottish Government to get on with that."
A Scottish Government spokesman said: "We recognise the complexities and difficult circumstances that the council has faced as it seeks to make the right decisions for the people of Edinburgh.
"It is appropriate that ministers now give full consideration to all of the factors before making any further decisions."
The Liberal Democrats won support from their SNP coalition partners to get the project nodded through, despite the Tories calling for the contract to be cancelled.
City leader Jenny Dawe hit out at Labour and Conservative councillors, who came together last week to force through the shock decision to stop the tram line at Haymarket.
She said: "To play political football with the citizens of this city shows irresponsibility of a level never before seen in this Chamber.
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