The Hammers conceded a penalty early in the second half, which was converted by Eden Hazard, before centre-back James Collins volleyed home to level it up on 77 minutes.
But Diego Costaproduced an 89th-minute winner for the Blues which in the end gave them a deserved three points according to a frustrated Bilic.
"Of course when you concede so late in the first game it leaves you disappointed and is a big frustration for us," Bilic said.
"We were so close against a top side on their ground, but they deserved it.
"We were so close and we thought that's it, but let's be honest, apart from the first 15 minutes and from the time we equalised, they were better than us. They didn't create many chances, but we gave them the penalty from our ball possession and the second goal was like that as we had the ball totally under our control in the middle of the park.
"They were much more aggressive than us, they were there and winning the second balls and, on top of that, they have players like Hazard who were on form and on fire. You have to admit they were better than us.
"From the moment we equalised and from there we were in control of the game as they lost their shape and changed their system and were playing long balls, which I expected us to cope with a little bit better, but then they scored a good goal."