Amadou Onana and Jhon Duran had Villa 2-0 ahead, before Leicester attemped a late fight-back after Facundo Buonanotte's goal.
Afterwards, Cooper said: “I thought we looked a good team at times today. We definitely didn’t deserve to lose the game. For the first goal, we need to own the set play – but it should never have been a free-kick.
“We’ve not just gone toe-to-toe with a Champions League team, we’ve also looked a better team than them. It’s a tough one to take. It’s three games now without a win, which is obviously not what we wanted.
“In the three games we’ve seen, we’ve seen more than enough in the performances to feel like we’re going to be OK. We’re disappointed with the defeat, but if we stay as we are and improve in areas we want to, we’ll be all right.”