The Turkish club held the Gunners to a goalless draw in last week's first-leg play-off in Istanbul but created enough openings to have won the game.
Bilic still has some regret over his team's failure to convert their chances into goals, particularly after the second-half dismissal of Aaron Ramsey, but he has taken great encouragement out of the fact that his players no longer have any fear of facing such illustrious opponents.
"We showed from our performance in the first leg that we are capable of giving them a game. We played well," said Bilic.
"We had our chances and they had theirs. We were not totally happy with the result as I think we deserved to win, but we go into this game full of confidence.
"I was confident and my staff were confident before the first game. But maybe some of our players had a little bit of doubt because they had not played against those so-called 'big guns'.
"But after the game they were very confident, which I don't mind as long as you do not become big-headed.
"We are not the favourites. They are the favourites – they are Arsenal – but we have a dream, a hope.
"It's more of a plan, though, and we are going to do everything we can to fulfil it. We have prepared our game, our plan. I have big belief in my assistants and they are going to do the job."