The visitors thought they should have had a penalty when Ben Chorley brought down Liam Dickinson but Cook waved away their claims.
Poyet was dismissed from the dugout for his vigorous protests and the Uruguayan's misery was compounded when Scott McGleish grabbed an equaliser for Orient eight minutes after the break.
Williams said: "We have to be satisfied with a point because that is what we have got. You have to say it was a very close game, and I can see why Brighton have done so well away from home.
"They were a real handful on the break and caused us an awful lot of problems so I would say a draw is a fair result."
Williams added: "If a penalty had been given (against Chorley) I am sure it would have been followed by a red card. You could question an awful lot of decisions but if you do that you get into trouble and it costs you money. And I have got a wife and kids to feed. Gus obviously disagreed with the decision and I probably would not disagree with Gus."