Albion took the lead after 17 minutes when full-back Phil Edwards found a way into the penalty area, turning and finishing low under goalkeeper Scott Flinders.
Edwards then turned hero as he cleared off the line by Andy Monkhouse, who was then also denied by Ian Sharps.
But Bradley Walker cracked home a leveller after 69 minutes to ensure Pools claimed a share of the spoils.
"It's a point for us and am I pleased?" Cooper asked. "The message we went out with having watched Burton was that they like to get on the front foot and press teams.
"We had to move the ball quicker and play between them more, get forward on the front foot quickly.
"We didn't do it enough in the first half. Second half was a lot better. The message was the same from us both halves.
"They are a form side, we accept that, but if we went about our business first half we could have got in front and won the game.
"They are a side feeling good about themselves and we could see that.
"But we showed some resilience to come back. Burton created openings, but I didn't see anything I feared. The plaudits we have had for passing the ball, we didn't do it this time and we didn't create a forward momentum."
Walker's classy first-time finish helped turn the game in Pools' favour, and Cooper added: "The introduction of two substitutes gave us that impetus and they made changes to try and see it out 1-0.
"Bradley's goal was smashing and, we say it again, but only one team was going to win it after that, but we couldn't find a second.
"We had one flash wide, one off the line - maybe not quite enough again."