The manager saw his Besiktas side beaten 1-0 on aggregate in their play-off tie but does not feel the Gunners are credible challengers for the trophy this season
Arsenal limped into the group stages of the competition with a 1-0 aggregate play-off success on Wednesday night thanks to Alexis Sanchez's first goal for the Gunners.
The victory means that Arsene Wenger's men will compete in the competition proper of the Champions League for the 17th straight season, but Bilic does not view the 2006 finalists as challengers for this season's trophy.
"I would love it [Arsenal to reach next year's final in Berlin] because it would make us look like contenders," Bilic told reporters.
"If they improve [they have a chance], and of course they are going to improve, the league just started and they have got a few injuries.
"They are missing the strikers although Sanchez was good tonight. But to win it? With Bayern [Munich] and Real Madrid? Football is strange but it would be difficult."
Arsenal will discover their group-stage opponents at Thursday's draw in Monaco.