[I]t is necessary to believe that sins neither are remitted, nor ever were remitted save gratuitously by the mercy of God for Christ's sake; …
We cannot by means of anything that we do obtain forgiveness for our sins. It's impossible. Consequently it's not possible for a man to save himself.
It seems to me, though, that the rest of this chapter of the Decree addresses the errors held by Protestants by which they might judge the Gospel and reach their false conclusion.
…yet is it not to be said, that sins are forgiven, or have been forgiven, to any one who boasts of his confidence and certainty of the remission of his sins, and rests on that alone; seeing that it may exist, yea does in our day exist, amongst heretics and schismatics; and with great vehemence is this vain confidence, and one alien from all godliness, preached up in opposition to the Catholic Church.
This is an explicit rejection of the fiduciary notion of justification held by Protestants: no man's sins are forgiven merely because he trusts that they have been. No. And just so that there's no misunderstanding, they make things even more clear:
But neither is this to be asserted, – that they who are truly justified must needs, without any doubting whatever, settle within themselves that they are justified, and that no one is absolved from sins and justified, but he that believes for certain that he is absolved and justified; and that absolution and justification are effected by this faith alone…
St. Robert Bellarmine is reputed (I have no source for the quote, so I can't substantiate it) to have said that the greatest Protestant heresy was their idea of assurance, which Trent condemns here. Worse, they make doubts about the matter into a deadly sin, so that it's like unto doubting Christ's work of atonement and God's promises:
…as though whoso has not this belief, doubts of the promises of God, and of the efficacy of the death and resurrection of Christ.
In the end these ideas reduce the Gospel to a matter of subjectivism: it's all within the individual man.
This is not to say, of course, that doubts about God's promises are warranted:
For even as no pious person ought to doubt of the mercy of God, of the merit of Christ, and of the virtue and efficacy of the sacraments…
Our salvation is not a subjective thing; consequently we ought not to doubt.
…[nevertheless] each one, when he regards himself, and his own weakness and indisposition, may have fear and apprehension touching his own grace; seeing that no one can know with a certainty of faith, which cannot be subject to error, that he has obtained the grace of God.