The visitors went in front through Jacques Maghoma and held it until Marc Richards rescued a deserved point with his fourth goal of the season although Chesterfield had Jack Lester sent off in stoppage time.
"In the first half, we were awful, we were abysmal," Cook said. "You've got to respect Burton, they came here with a game plan and in the first half it worked well in the game
"But as we are learning, it's important that you stay in games and we can't play well all the time. Eventually we know we will get a spell in the game and I think we dominated the second half.
"We were terrific, we put a lot of quality in the box and should have scored more than one goal.
"But what I was pleased with was we didn't lose and the level of performance in the second half was more than acceptable."