The Magpies emerged as comfortable winners on the opening day of the Premier League season with a 2-0 victory in front of a sellout St James’ Park.
Supporters watched on as a dominant United remained patient before Fabian Schar broke the deadlock with a stunning long-range strike on 58 minutes.
Callum Wilson then added a second 12 minutes before the end when he cleverly flicked home Joelinton’s low cross.
Forest, playing their first Premier League match since 1999, failed to register a shot on target, compared to Newcastle’s 10.
“No one can be pleased when we lose a football match so we’ll not lose sight of that,” Cooper said after the game.
“Newcastle deserved to win the game, they were the better team. We’ll always show respect to that.
“They had a lot of the ball, a lot of territory and overall, I thought we were OK with that.
“They got into a lot of good areas and good positions but they didn’t really pepper Dean (Henderson) in goal. It’s taken a 25-yard strike to beat us.
“Where we weren’t right today was our in possession. We turned the ball over too much and we didn’t make enough passes when we could.
“In the end, that’s cost us, even with the two goals.
“The first goal came from a corner in the second and the way we gave the ball up before that is not what we want to do.
“We fell short today in our performance. We have to live and learn from that. “
Newcastle enjoyed 61% possession, having 23 shots in total.
Cooper added: “What was important is there has been a lot of talks among the players about Premier League football.
“We’re disappointed we’ve lost a football match today but, at least we felt the difference of what a Premier League game is. There is a big difference, for sure.
“We have to reflect on that quickly and get used to it.”