Having already suffered close defeats at Arsenal and Manchester United in the opening weeks of the Premier League campaign, a win in west London would have pleased Cooper.
Asked if the belief from the performance at United had helped his players heading into the game at Chelsea, he replied: “Yes, I definitely think that – and also the frustration.
“We took that into the week and the guys spoke quite passionately in the dressing room after the (United) game and I reminded them of what some of them said in the build-up to this one and fair play to them, they took that into today.
“We knew it was going to be the type of game that it was – you don’t come here to plan to dominate possession and have chance after chance, but if you do certain things well you can create chances and keep a clean sheet. That is how it unfolded.”
Cooper reserved special praise for Joe Worrall, the Forest captain putting in a fine display just days after the death of his police officer uncle.
“He’s been incredible,” Cooper said of his skipper.
“I personally have known what was going on before it came to public (knowledge) and he’s put his family second for the football club.
“I think the club has helped them in terms of giving them a bit of a release and the guys just showed him a huge amount of respect in the dressing room after what he’s been through.
“I cannot speak highly enough of the man that he’s been over the last week or so. I know how important today will be for him and it will give him and his family some respite because nothing can really make what happened any better, but at least it gives them some nice feelings.”
Defeat for Chelsea means they have won just one of their first four league games under Mauricio Pochettino.
The head coach stuck with the same starting XI that beat Luton last time out in the Premier League but was also able to turn to Noni Madueke, new signing Cole Palmer, Ian Maatsen and Mykhailo Mudryk off the bench as Chelsea searched in vain for an equaliser.
“We were not clinical in both areas,” Pochettino said of the Chelsea performance.
“We made a mistake and then we created opportunities, but if you don’t score it is difficult to win games. This type of game I think will help us to be more mature, it is not only about having quality, it is also about competing in different ways.
“Of course we can’t say that we didn’t deserve more, but in football the stats sometimes reflect what you do and in that case we created but we didn’t score and we only had a few shots on target.
“We are building something and it is always up and down. We are unlucky because I think we deserved more against West Ham and today – but I have said before, it is only a matter of time.”