Arsenal are out of the competition after defeat to Club Brugge on Wednesday.
Demiane Agustien had Arsenal ahead before Yanis Musuayi and Jakke Van Britsom struck for Brugge. Arsenal also had Mishel Nduka on 32 minutes.
Horseman told the club's website: "I think my initial thoughts are for such a young group, real pride. It’s a huge learning experience; we obviously made a conscious effort in the last couple of games to go with a young squad. Some of these lads are 14 or 15 years old and I was so proud of them.
"What we've probably learnt this season from it in total, but particularly today, is how you manage a game. It’s 1-1, we've been down to 10 men for 60 minutes. We had the chance to manage the game better, in really tough conditions.
"I think we were more than competitive. We showed more than enough in certain individual areas to know that it was the right decision in the last couple of games to do what we did and give experiences to younger players."