Lys Mousset's first-half strike gave a determined Blades outfit the win in front of their adoring fans at Bramall Lane.
Arsenal attempted to break down Chris Wilder's side in the second-half but clear cut chances were few and far between.
But Emery thinks the Gunners were unlucky not take something away from the game.
He told Sky Sports: "We did not deserve to lose and we conceded a lot of corners in the first half and they scored in one action.
"Above all, we have to improve by not allowing balls like that. When we have our opportunities to attack, we created more chances than them but did not score today.
"We deserved more from the game but they have conceded the least goals in the Premier League and it was going to be difficult if they scored first.
"We tried in the second half, created three good chances to score.
"We did not deserve to lose and we will think about where we can improve. When we were losing 1-0, we controlled the game but and defended well but they had a lot of players in their box so it was difficult to achieve attacks. We created three or four chances and we spoke about scoring one goal, we could have controlled it better if we did.
"We have challenges in each match. Tonight we had a big challenge to get the three points. We are playing some young players who are taking experience but the most important thing is to win. The result is one thing, but we can analyse positively."