Frontrunners Schal and a joint venture between Citex and Mace were stood down after the assembly opted for a fixed-price contract for the opera house.
A spokesperson from Mace expressed disappointment at the decision. He said: "We are now resigned to the fact that the project will not be going down a construction management route.
"It is very disappointing for all of our staff because it's not every day you get to work on building an opera house." Schal refused to comment on the decision.
Edwina Hart, the assembly's minister for finance, said the decision was made because the assembly needed to ensure price certainty.
She said: "The project simply cannot go forward on the basis of an assembly blank cheque. Frankly, were these projects to start under construction management terms, it would be extremely difficult to resist demands for further funding.
The project cannot go forward on the basis of a blank cheque
Edwina Hart, finance minister
"We could be signing up to a level of capital support amounting to £37m at least – but with no limit to our financial exposure." The project could be further delayed by a planned period of market testing for the fixed-price procurement method.
However, the assembly said the market testing could result in tenders above what is affordable.
Last week, Sir David Rowe-Beddoe, who is standing down as chairman of the Welsh Development Agency, took charge of the project.
The construction management decision is the latest setback to hit the scheme. Last September, rising costs and a budget review persuaded main contractor Amec to abandon the job. A month later, Cardiff council stepped in to buy the project site for £2.5m after landowner Grosvenor lost patience with the project client and put it up for sale.