The Gunners travelled to Belarus on Thursday night as the heavy favourites for the game but they were left stunned at the end of the first half.
Emery's men had missed a number of chances before BATE midfielder Stanislav Dragun headed home after some lazy defending from a free-kick.
Arsenal never did enough to grab an equaliser and their night got worse when Alexandre Lacazette was sent off for an elbow in the 85th minute.
Emery insists the second leg of their last-32 tie will be different but he has warned his team they need to learn to control their frustration levels.
He told reporters: "It's the first match. We are going to play another 90 minutes next week and I'm sure it's going to be different.
"I didn't see the action but we need to control the frustration. It's bad news, this red card. Next week we won't play with [Lacazette]. But it gives chances for another player."