Bilic stated that he was delighted with the derby win over a side he believes will be title contenders this season.
“Not only for the three points but points against a team that are the title contenders,” Bilic was quoted as saying in the Express.
“If you add to that a London derby, it makes it a even bigger win. This is very special. I am very proud of the second half performance.”
Arsenal finished last season in third place and have not won the league title for over a decade but have been tipped as one of the favourites to land the championship this season.
The victory over the Gunners was made even more special for Bilic as it broke his poor record managing major derby games.
Bilic was a fan favourite at Besiktas but failed to win a derby game in his two-seasons in charge of the Black Eagles.
Bilic resigned from his position as Besiktas manager at the end of the season and replaced Sam Allardyce as West Ham boss.
West Ham take on Leicester City at home next on 15 August 2015.