They warned a call by green groups and transport campaigners for the project to be investigated by the Auditor General before contracts are let would simply delay a vital link in Scotland's infrastructure.
In a joint letter, released as MSPs were passing the legislation to allow the 2 billion crossing to proceed, groups including the Green Party, Friends of the Earth, WWF and Transform Scotland called for an urgent investigation into the background to the new bridge and the alternatives to it.
Scottish Green leader Patrick Harvie said: "In 2008 a report for the Forth Estuary Transport Authority showed that the existing bridge could be repaired for a maximum cost of 122m, a saving of more than 2bn just as budgets are being squeezed hard. We are therefore calling on the Auditor General to help make sure Scotland isn't blundering into the biggest mistake of devolution."
Former Edinburgh council leader Keith Geddes, who also signed the letter, pointed to a legacy of capital projects which he said had suffered from inadequate forward planning.
"The new Edinburgh Royal Infirmary, the Scottish Parliament project and of course the now infamous Edinburgh tram project are prime examples of projects that have not only increased the burden on the taxpayer but have put question marks over Scotland's ability to deliver major capital projects."
However, Ron Hewitt, chief executive of Edinburgh Chamber of Commerce, said the disruption caused by the closure of the existing bridge because of snow had shown how vital the link across the Forth was.
He said: "There are always people who don't want roads of any kind. When the bridge was closed the other day we had enormous problems getting people into work from Fife.
"This kind of move will just delay the bridge getting built.
"The decision has been made. The sooner they let these contracts the better."
Transport Minister Keith Brown said the new bridge was "absolutely vital to ensure Scotland's economic well-being".
The Bill was passed by 108 votes to three.
Edinburgh West MSP Margaret Smith said she accepted the need for the bridge, but joined the Greens in voting against the Bill because it did not represent the best deal for her constituents.
She said: "I am disappointed my amendments to safeguard residents' rights in relation to noise were not supported.
"There is a real sense of disappointment and some anger amongst my constituents, who feel that they have been ignored.
"We called for a tunnel and got a bridge; we called for a direct link to the M9 but have been denied that. We were promised a multi-modal model but this scheme does not deliver on that either. The design we have will result in increased traffic and noise from the time of construction."