Bilic's men produced a fine performance to claim a draw with the champions having been beaten 2-1 by relegation-threatened Newcastle United last time out.
Enner Valencia opened the scoring in the first minute before Aguero equalised from the penalty spot eight minutes later, having been brought down by Carl Jenkinson.
Valencia restored West Ham's advantage 11 minutes into the second half, only for Aguero to hit home his second nine minutes from time.
READ MORE | Hart: Man City didn't deserve win
Cheikhou Kouyate hit the crossbar with a header late on, leaving the teams to settle for a share of the spoils.
"I didn't see the penalty – from here it looked soft, but I was far, far away," Bilic told BBC Sport.
"It was a great game of football. I'm so proud of our team and Man City. There was everything in it. Four goals, chances, yellow cards and a penalty.
"We defended well and created many chances. We hit the post at the end, but they hit the post twice.
"We were a little bit disappointed, but I said to the players they shouldn't be. But if you are disappointed after playing [and drawing against] Man City then that's good."