The 27 year old Italy international said it was talks with Bilic, as well as the promise of first-team football, that convinced him leave the relative comfort of Italy's top club.
"I talked with the manager and he explained to me what he wants to do with this club," Ogbonna told Press Association Sport.
"The manager sold me the story and I feel it is better for my career to come to West Ham now. I know I will play now and I don't think about last year. I have to think about this year.
"I am very happy but it (the Arsenal win) was only the first match so we are looking forward and not just thinking about what we did in the first match. We knew it was a difficult game but there are a lot of difficult games so we have to concentrate on the next game and take things step by step."