West Ham rarely looked like threatening Thibaut Courtois's goal until James Collins scored with the Hammers' first shot on target in the 77th minute.
And even Bilic had to admit that Chelsea were the better side on the course of 90 minutes.
"It's a big frustration for us because we were so close against a top side on their ground. But they deserved it," Bilic said. "Let's be honest -- apart from the first 15 minutes and from the time we equalised, for that period of about one hour they were better than us.
"They didn't create many chances but they had that individual class. Not only that, they were much more aggressive -- they won the second balls and if you add on top of that players like Hazard on top form, I have to admit they were better than us.
"I'm more disappointed with the late goal than with the incident with Costa. We didn't play well and we can do much better."
West Ham also suffered a blow when new signing Andre Ayew had to come off in the first half after suffering a thigh injury.
"We have to wait on Andre Ayew," Bilic said. "It is a thigh injury and we will find out after the scan tomorrow.