Pep Guardiola's City beat the Hammers 3-1 at the Etihad Stadium and despite keeping up with them at certain stages, Bilic is of the belief that the home team possess a lot more quality than his.
"Second half we played good and created chances because we opened up. The team showed character, showed spirit," he told Sky Sports 1.
"They were deservedly two goals up but in the second half we played much better.
"We were close to them, we were closing them down. We were winning balls, we were winning second balls. Then, after we scored it gave us hope and we had our moments to equalise.
"But they are different class to be fair, especially when we play without six, seven, eight players."
Raheem Sterling scored an early goal while Fernandinho made it 2-0 to City before Michail Antonio pulled it back to 2-1 for the visitors, prior to Sterling adding a second from an acute angle in injury time.