Mark H Durkan was minister when he opted to issue an enforcement notice rather than a stop notice.
Companies were able to appeal against it and keep extracting sand pending the outcome of the ongoing appeal.
Environmental group Friends of the Earth took the department to court over that decision.
Lough Neagh is an internationally important bird sanctuary with EU protection.
The court of appeal ruled that, in the absence of proof that the dredging was not doing any harm to the lough - the so-called precautionary principle - the minister had taken the wrong approach.
"What has been disregarded in the letter of decision, where it deals with the Stop Notice, is that these operations, are considered likely to have significant impact, that the nature and extent of that impact has not been established, that prior to the grant of permission is the requirement to establish that there will be no significant impact and that it is imperative that the precautionary principle be applied," the judgement said.
The judges referred the decision back to the Department for Infrastructure for reconsideration.
This ruling does not mean that sand dredging must stop immediately.
But Friends of the Earth has said it would be writing to the department on Wednesday with a copy of the judgement demanding the issuing of a stop notice.
Around 1.5m tonnes of sand is taken from the lough every year by five companies.
It provides around a quarter of the sand needed for construction in Northern Ireland.
A former environment minister took the wrong approach when he opted not to immediately stop sand-dredging on Lough Neagh, the appeal court has found.