Ryan Yates had given Forest a 16th-minute lead, only for Jamie Vardy to level for the hosts. But in the second-half, Chris Wood took over to strike twice and leave the Foxes in 14th place on the table.
Cooper said afterwards: “It's self-inflicted, no doubt about that, and it's on us. We all have to take responsibility for how the game panned out.
"We made poor mistakes for the goals, no doubt about it, and we were punished for it but I just think conceding so early on in the second half was obviously not a good thing.
"There was still a lot of time for the game to settle again, us to carry on with things we were doing in the first half, improve and be the threat we wanted to be.
"The third goal was just a real killer and still there was a lot of time left but the game just became a little bit of trying to get players on in certain positions, territory all that stuff, defenders on, extra attackers on, we just lost any sort of rhythm we got in the first half - we lost it completely because of scoreline so it's on us.
"We have to take responsibility for it. It's a setback after winning a few games coming into this. We have to accept it, completely on us and me and we’ve got punished for the poor giveaways on the goals.
"Conceding so early in the second half was far from ideal but I still felt ‘ok let’s recover again’, we had some good control in the game and painting some pictures at half time, where we felt we could do even better and maybe there was a little bit of not panic but probably a little bit of trying to put things right maybe too soon rather than sticking to plan, keeping going believing we would get the game how we wanted it to be.
"Forest are a counter-attacking team, they are really good with it and we gifted them moments for them to show that."