The Cherries couldn't spoil the party for the Hammers in their first Premier League fixture at the London Stadium, and Cook feels the goal could have been avoided.
"We've worked on defending crosses all week. We let that cross come in and then he was there at the back stick.
"We didn't help Smithy out with the cross, he was one on one and then to have a free man at the back stick, that can't happen at any level."
Harry Arter was dismissed for a second bookable offence in the second half, forcing the Cherries to play out the final 13 minutes with ten men.
And Cook believes that the numerical disadvantage had a defining impact on the outcome of the match.
"The sending off was huge - it changed the game," the defender continued.
"I felt we were the stronger side in the second half, so it's hard to take. I felt we were pushing to get the winner.
"Even to have kept a clean sheet would have been brilliant. We need to learn quickly. Two games and no points, it's very disappointing."
