The Gunners slipped to a shock 1-0 loss in the first leg of the last-32 tie, their misery compounded with the late dismissal of Alexandre Lacazette for violent conduct.
Ozil and Juventus-bound midfielder Aaron Ramsey did not travel for the game in Belarus, with the absence of the former turning into one of the main talking points in Emery's post-match media conference.
However, the former Sevilla boss made clear that Arsenal had prospered without Ozil in their win over Huddersfield Town at the weekend, insisting the side he picked to face BATE was good enough to get a positive result on the road.
"Every player is okay to play. Those that were here, we can win with them and we deserved that," said Emery, a three-time winner of the competition with Sevilla.
"Last week we won and we played with the same players. No different performance. We deserved to win but didn't get the result. They were very organised.
"We can win with every player and lose with the same players."
6 - Arsenal have been eliminated from each of their last six two-legged ties in European competition when losing the first leg – the last such tie they managed to reverse was against FC Porto in the Champions League in 2009-10 (6-2 on aggregate). Delicate. pic.twitter.com/H7FarQiG2k— OptaJoe (@OptaJoe) February 14, 2019
Despite the setback, Arsenal will be confident of overturning the one-goal deficit in the return fixture at Emirates Stadium next Thursday.
Emery promised an improved performance on home soil after Stanislav Dragun's header on the stroke of half-time clinched BATE a famous win in front of their own fans.
"It's the first match. We play the next match in London and I think it can be different," added the Spaniard.
"I trust in our players and in our stadium with our supporters. I trust in our work and preparations to make a different result.
"It is not the result we wanted. We deserved more but they worked for this. Next week is going to be different."
On Lacazette's dismissal for elbowing Aleksandar Filipovic, Emery claimed he did not see the incident but had warned his players about staying calm when chasing the game in the second half.
"We spoke about how we needed to control the frustration," he said. "It's bad news, the red card. We are not going to play with him next week."