Lacazette, who had earlier seen a goal chalked off for offside, was shown a red card five minutes from the end of the game in Belarus after elbowing BATE defender Aleksandar Filipovic.
He will now be suspended for the return leg at home next week, with Arsenal needing to overturn the aggregate deficit in order to keep progressing in the competition.
"Letting the team down like that is the worst feeling," the Frenchman tweeted afterwards.
Letting the team down like that is the worst feeling..— Alexandre Lacazette (@LacazetteAlex) February 14, 2019
I should have stayed calm but it’s not always easy.. Sorry
There are still 90 minutes to play and I believe that my teammates will make it to the next round.. #COYG #Laca
"I should have stayed calm but it's not always easy.. sorry," he added. "There are still 90 minutes to play and I believe that my teammates will make it to the next round."
Gunners boss Unai Emery admitted that Lacazette need to be more in control.
"I didn't see the action but we spoke and frustration needs controlling. It's bad news with the red card. Next week we aren't going to play with him but now we are going to think with the players that are OK for next week," he is quoted as saying by BBC Sport.
With the Premier League paused for the FA Cup fifth round this weekend, Arsenal don't actually have another game until the return leg with BATE at the Emirates Stadium, giving Emery and the squad a full week to prepare.
After that, clashes with Southampton and Bournemouth close out the month of February.
Source : 90min