The match saw Josh Ogunnaike score for Arsenal, but the visitors went ahead 2-0 after Olympiakos' goals were scored following a red card shown to Louie Copley.
Horseman noted that the team's mistakes led to the goals, which came at a critical time when Arsenal was gaining control of the game.
He stated that the red card disrupted the team's momentum, making it difficult to recover from the 2-0 deficit.
However, Horseman praised his team's second-half performance, highlighting the impact of the wide players and Kyran Thompson's impressive link-up play.
Although the team was ultimately disappointed with the result, Horseman believed they should have at least drawn or potentially won the match if they had been more effective in the final stages.