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.
"If you asked even the Orient supporters they will let you know it was a penalty. That was a penalty and a red card," said Poyet.
"The referee is 10 yards away and doesn't give it. I got sent off for asking why he didn't give it. It's my mistake and I take it but I don't apologise for what I have done."
Striker Nicky Forster was left out of the squad, yet Poyet said: "I want to talk about the players who were here."