The coach 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
The Gunners limped into the group stages of the competition with a 1-0 play-off success climaxing on Wednesday thanks to Alexis Sanchez's first goal for his new club.
The victory means that Arsene Wenger's men will compete in the competition proper of the Champions League for the 17th straight season, but the Besiktas coach does not view the 2006 finalists as challengers for this season's trophy.
"I would love it if Arsenal to reach next year's final 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 to compete against? Football is strange but it would be difficult."
Arsenal will discover their group-stage opponents at Thursday's draw in Monaco at 17:45CET.