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Antony Sweeney gave Pools' a 23rd-minute lead and although Jamal Campbell-Ryce equalised for Orient before the break, Liam Noble struck the home side's winner in the 73rd minute.
Cooper said: "I asked the players for a performance and I'm happy with the result. We started really well, but there is a soft side to this side.
"We went in front, then conceded and I saw a negative, a nervousness creeping in.
"Their goal has come from a bad mistake, we gave the ball away. It was scrappy at times and some of the boys looked like they had never seen a football.
"I'm just really pleased to get a win - I didn't enjoy it to be honest. We have to be better and I understand the fans' frustration."
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