The Foxes are back in the Premier League but have endured a tough time under the ex-Nottingham Forest coach.
Cooper took over from Enzo Maresca in the summer, with the Italian joining Chelsea.
Asked about beating Bournemotuh last time around, he stated: “I feel happy for the players, equally as happy for the supporters and staff.
"It was always going to be important to get the first win back in the Premier League. I’ve seen many win here, I would have loved for it to be sooner, we know that.
"We could have done some things better but we’ve also been unlucky, so I’m just glad everything went well. It’s great to win but we have a lot of work to do to be a force.
“It’s an international break and the work continues and now we need to be completely obsessed with beating Southampton in a couple of weeks.”
Cooper added: “I’ve got to build trust here, it’s clear I have work to do with people really believing in me and I’m fine with that.
“That’s my really big motivation because it’ll show how much I really want to be here and how much I want to get this job right with the players.
“Feeling the atmosphere here, it’s been good. We really needed the supporters in the second half and there were times when the crowd backed us.
"We needed that. It’s great to win but I know I have a lot of work to do so the team become a force – it’ll take a lot of work.”