The City Ground had not hosted a top-flight match since 1999 and Taiwo Awoniyi ensured it was a winning homecoming for Forest with his first-half goal.
The striker, who until Saturday night was the club’s record signing this summer, bundled home from close range to become the first Forest player to score a Premier League goal since Chris Bart-Williams all those years ago.
The Forest fans had waited a long time for that moment and Cooper was aware of the importance.
“There were two things today, the occasion, the event of the first home game back in the Premier League, so important to so many people and we were never going to treat it as a normal game, it was more than that,” he said.
“You could sense since we got promoted everyone was waiting for the first home game.
“We knew it was a very important day. We spoke about three generations of Forest supporters here today, one who remember the really good old days, a new generation who will be watching their first Premier League game and the ones in between.
“We had to represent all three of those today.”
Awoniyi’s goal in first-half stoppage time, which came moments after West Ham had a goal ruled out by VAR, was reward for a spirited first-half display.
The second half was more frantic with Forest goalkeeper Dean Henderson saving Declan Rice’s penalty while Pablo Fornals and Said Benrahma both hit the underside of the crossbar.
Cooper felt his side deserved it for the opening 45 minutes.
“First half I thought we were much the better team, we really took the game to West Ham,” he added.
“In terms of the game, I was so happy with our attitude and confidence going into the first half, the atmosphere was amazing anyway but that raised it even more.
“We played really well in the first half and maybe we should have created more. We deserved to win the game today and it was important we did.”
Hammers boss David Moyes was left to curse his side’s luck after they slipped to a second successive defeat.
“I’m really frustrated,” he said. “We haven’t scored many in pre-season so that was an excerpt of it.
“The first 20 minutes frustrated me, I thought we were really poor. We grew into the game. We didn’t deserve the result we got that was for sure but we did in the end.
“Forest started well, they were powerful, strong and put us under pressure. We didn’t cope with that well.
“Maybe on another day, today we hit the underside of the bar twice, we missed a penalty, we got a goal disallowed which was a bit contentious.
“Today very little went our way in what was a big game for Nottingham Forest. They carried quite a bit of luck and we didn’t have any.”