The Foxes were drawing 2-2 before the Gunners struck twice in injury-time via an own goal from Wilfried Ndidi and Kai Havertz.
Cooper said: "Tough one to take to be fair. Proud of the second half performance particularly. If it's a team that's not together, they can really go under after the first-half but it was great to score as early as we did in the second half and then go to 2-2.
"You know you are going to suffer here at time against a really good time like Arsenal at the Emirates but I felt like we were coping really well. To have that deflection for the third goal is just a bit of where our luck is but then the fourth goal is against the run of play.
"It's another loss and the results always write the narrative but there was so much to be positive about, particularly in the second half and we've got to try and keep going keep capitalising on what is going okay and just improve."
On what was said at half-time, Cooper said: "Just to stick with it to be honest. It was disappointing with the way we concede the goals because they are typical Arsenal goals with the cut-backs, we've done a lot of work trying to deal with that. I don't want to make the headlines around referees because I'm trying to take responsibility for a team trying to do better in the Premier League but it's a clear foul on Jamie Vardy for the first goal and the left-back (Riccardo Calafiori) has to get sent off for a second yellow but there's so much more we could say, the whole game knows but I'm not going down that road today."
On James Justin's second goal, he said: "Great goal, straight off one of the moves that we work on in terms of where we want people to get the ball. It's a brilliant finish. Good to see that come off. Just a pity that it didn't mean more in the game."
On Mads Hermansen's saves, the manager added: "We're really happy with Mads, he's a talented young goalkeeper and he is on the right path. He didn't deserve to concede that third goal with the deflection but it can happen unfortunately. He didn't deserve to concede a goal like that, neither did the rest of the guys.
"You have to stand up, you have to keep believing in what you are doing. These are the demands of the Premier League. We fell on the wrong side today."