Mr Cook's remarks, to the cross-party Commons select committee on Foreign Affairs, could give pro-European Tories a let-out clause to abstain or vote against the treaty.
Mr Cook said: "There was one major disappointment - that is that we failed to reform the institutions of Europe in preparation for the larger Europe which will follow the enlargement to central Eastern Europe and Cyprus.
"We have not tackled the size of the Commission, which plainly cannot go on growing with every new country; nor have we addressed the weighting of the votes in the council as they are counted for qualified majority voting.
"On present weighting we are approaching the nonsensical outcome in which countries representing a majority of the population of Europe would not be able to muster a blocking minority on qualified voting. That is plainly undemocratic, not sustainable and will have to change."
He added: "Unfortunately we failed to get a consensus for change in Amsterdam. It foundered on the resistance of the smaller nations to countenance a re-weighting ... At 4am we found ourselves at an impasse. It was important for enlargement that we should not founder at Amsterdam, because enlargement talks could not begin until we had completed the IGC."
John Redwood, the Tory trade and industry spokesman, said: "I am delighted he is criticising the treaty. I invite him to join us in the `noe' lobby. I don't agree with him that it marks the high tide of integrationism. It is another move up the beach."
Mr Blair and Mr Cook took over the negotiations, at an advanced stage, from the Tories after the election, and his criticism of the outcome was not intended as an attack on the Prime Minister.Reuse content