Stewart Stevenson reacted to comments that the lifespan of the current road bridge over the firth at Queensferry could be extended further than has been predicted, reducing the need for an immediate and costly project.
Facing questions from Holyrood's Forth Crossing Bill Committee, he said deterioration to suspension cables cannot be "undone" and that traffic flow has increased significantly since it was built in the 1960s.
Mr Stevenson added: "It would leave us, if we were to take our foot off the accelerator, with no option if the outcome is other than the most optimistic.
"It is very clear that we must continue to make best progress, otherwise future generations of the people that we serve will certainly not thank us."
The committee is investigating details before legislation is passed to give ministers the authority to construct the bridge and associated road works, estimated to cost about 2 billion.
Convener Jackson Carlaw sparked the minister's warning by asking if the project would have been regarded as so "time critical", given suggestions that remedial work may have extended the existing bridge's lifespan.
Two bids have been submitted to take on the project, described as the biggest since devolution 10 years ago.