The Ukrainian champions were convincing 7-0 winners in Belarus last time out as they picked up their first victory of their Group H campaign in stunning fashion.
Luiz Adriano became Shakhtar's all-time leading goalscorer with an incredible five-goal haul in that game, which moved Mircea Lucescu's side up to second in the pool.
For BATE, a defensive improvement is a must ahead of their trip to Lviv if they are to reclaim second spot, but defender Azevedo - a doubt for the game with a knee problem - has urged Shakhtar not to expect such a comprehensive victory this time around.
After a surprise 2-1 derby defeat to Metalurg Donetsk in the Ukrainian Premier League on Friday, third-placed Shakhtar have lost three of their last four following a positive start to their title defence.
And with their attentions reverting back to European competition, Brazilian Azevedo believes his team-mates need to be prepared for BATE's counter-attacking approach.
"We must always go out and win. Each match must end with a win in our favour. In the last encounter, we failed to do so," he told Shakhtar's official website.
"I hope that both against BATE and in subsequent Ukrainian league games, we will do better.
"In Lviv, they will fully focus on the counter-attacks. Probably, in the first leg, our opponents got a bit slack thinking that it would be easier for them at home. Now they are facing an away game."
Despite conceding 14 goals in just three Group H fixtures, BATE remain in with a shout of progression as they seek to emulate their exploits of 2010-11 when they reached the last 16.
Aleksandr Yermakovich's side will also be buoyed from their domestic efforts at the weekend, as a 2-1 win over Dinamo Minsk extended their unbeaten run in the league to 28 matches - breaking their own record in the process.
Both sides have injury concerns to contend with, as Yermakovich could be without Egor Filipenko (hamstring) while opposite number Lucescu has further doubts over Sergey Kryvstov (ankle) and Ilsinho (illness).
BATE captain Dmitri Likhtarovich could equal the Belarusian appearance record in UEFA competition held by Aleksandr Hleb, if he features for a 92nd time.
