One leading fund that started pulling out last year told a joint select committee investigation into the company that it had considered suing after a major profit warning.
MPs were told that Carillion's interim boss was able to give only "limited and vague" responses to key questions.
They said the company's annual reports were "worthless as a guide to the true financial health of the company".
The details come days ahead of a parliamentary hearing on Thursday when auditor KPMG will be asked about accounts that it signed off.
Carillion, which employed more than 20,000 people in the UK, went into liquidation last month after a series of profit alerts since last year sent its share price plummeting.
The company, which handled hundreds of public sector contracts including building hospitals and delivering school meals, was left saddled with debts worth £1.3bn and a pension deficit estimated at up to £2.6bn.
Nearly 1,000 workers have now been made redundant as part of the redundancy process and, though thousands of jobs have also been saved, there has been an additional knock-on effect for jobs among sub-contractors.
The collapse is being investigated by two parliamentary select committees and the inquiry has now published evidence it has received from investors.
Frank Field, chair of the Work and Pensions committee, said there was a "disconnect" between Carillion directors saying that "all was sunny" until it was hit by problems with a contract in Qatar.
"On the other hand, investors were fleeing for the hills, and it appears those who looked closest ran fastest," Mr Field said.
Rachel Reeves, chair of the Business, Energy and Industrial Strategy committee, said investors had "spotted that Carillion was heading for disaster".
"Carillion's annual reports were worthless as a guide to the true financial health of the company," she said.
"The fact that it was impossible to get a true sense of the assets, liabilities and cash generation of the business raises serious concerns about Carillion's corporate governance."
Kiltearn Partners, which held 10% of Carillion's shares early last year, began selling its holding in August.
It said in a letter to the committee that it believed there were "clear grounds for an investigation into whether Carillion's management knew, or should have known" about the need for an £845m provision against its construction business before that was announced last July.
The fund also said that if the company had not gone into liquidation it would have "considered participation in civil legal action against Carillion with a review to recovering a proportion of its clients' crystallised losses".
Kiltearn said that at a meeting with the company, interim chief executive Keith Cohcrane was only able to give "limited and vague" responses to "fundamental" questions.
Standard Life Aberdeen began pulling out of Carillion in December 2015 due to concerns about financial management, strategy and corporate governance that it had raised with the board until it sold up completely in July last year, MPs were told.